Give browsing contexts an explicit container

This is the first step for #5020.

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@@ -78565,6 +78565,9 @@ dictionary <dfn>DragEventInit</dfn> : <span>MouseEventInit</span> {
    <li><p>Set <var>element</var>'s <span>nested browsing context</span> to
    <var>browsingContext</var>.</p></li>
 
+   <li><p>Set <var>browsingContext</var>'s <span data-x="bc-container">container</span> to
+   <var>element</var>.</p></li>
+
    <li><p>If <var>element</var> has a <code data-x="">name</code> attribute, then set
    <var>browsingContext</var>'s <span data-x="browsing context name">name</span> to the value of
    this attribute.</p></li>
@@ -78581,31 +78584,43 @@ dictionary <dfn>DragEventInit</dfn> : <span>MouseEventInit</span> {
   context containers</dfn>.</p>
 
   <p>Each <span>browsing context container</span> has a <dfn data-export="">nested browsing
-  context</dfn>, which is either a <span>browsing context</span> or null.</p>
+  context</dfn>, which is either a <span>browsing context</span> or null. It is initially null.</p>
+
+  <p>Each <span>browsing context</span> has a <dfn data-x="bc-container">container</dfn>, which is
+  either a <span>browsing context container</span> or null. It is initially null.</p>
+
+  <p>Each <span>browsing context</span> <var>bc</var> has a <dfn
+  data-x="bc-container-document">container document</dfn>, which is the result of running these
+  steps:</p>
+
+  <ol>
+   <li><p>If <var>bc</var>'s <span data-x="bc-container">container</span> is null, then return
+   null.</p></li>
+
+   <li>
+    <p>Return <var>bc</var>'s <span data-x="bc-container">container</span>'s <span>node
+    document</span>.</p>
+
+    <p class="note">This is equal to <var>bc</var>'s <span data-x="bc-container">container</span>'s
+    <span>shadow-including root</span> here.</p>
+   </li>
+  </ol>
 
   <p>If a <span>browsing context</span> is the <span>nested browsing context</span> of a
   <span>browsing context container</span>, then the browsing context is said to be <dfn
   data-x="browsing context nested through" data-export="">nested through</dfn> the <span>browsing
   context container</span>'s <span>node document</span>.</p>
 
   <p>A <span>browsing context</span> <var>child</var> is said to be a <dfn data-export="">child
-  browsing context</dfn> of another <span>browsing context</span> <var>parent</var>, if all of the
-  following conditions hold:</p>
-
-  <ul>
-   <li><p><var>child</var> is a <span>nested browsing context</span> of a <span>browsing context
-   container</span> <var>element</var></p></li>
-
-   <li><p><var>element</var> is <span>connected</span></p></li>
-
-   <li><p><var>element</var>'s <span>shadow-including root</span>'s <span
-   data-x="concept-document-bc">browsing context</span> is <var>parent</var></p></li>
-  </ul>
-
-  <p>A <span>browsing context</span> <var>child</var> is then a <dfn>document-tree child browsing
-  context</dfn> of <var>parent</var> if it is a <span>child browsing context</span> and its
-  <span>browsing context container</span> is not just <span>connected</span>, but also <span>in a
-  document tree</span>.</p>
+  browsing context</dfn> of another <span>browsing context</span> <var>parent</var>, if
+  <var>child</var>'s <span data-x="bc-container-document">container document</span> is non-null and
+  <var>child</var>'s <span data-x="bc-container-document">container document</span>'s <span
+  data-x="concept-document-bc">browsing context</span> is <var>parent</var>.</p>
+
+  <p>A <span>browsing context</span> <var>child</var> is a <dfn>document-tree child browsing
+  context</dfn> of <var>parent</var> if <var>child</var> is a <span>child browsing context</span>
+  and <var>child</var>'s <span data-x="bc-container">container</span> is <span>in a document
+  tree</span>.</p>
 
   <p>A <span>browsing context</span> <var>child</var> may have a <dfn data-export="">parent browsing
   context</dfn>. This is the unique <span>browsing context</span> that has <var>child</var> as a
@@ -78627,10 +78642,10 @@ dictionary <dfn>DragEventInit</dfn> : <span>MouseEventInit</span> {
   group">group</dfn> (null or a <span>browsing context group</span>). It is initially null.</p>
 
   <p>It is possible to create new browsing contexts that are related to a <span>top-level browsing
-  context</span> without being nested through an element. Such browsing contexts are called <dfn
-  data-x="auxiliary browsing context" data-lt="auxiliary browsing context" data-export="">auxiliary
-  browsing contexts</dfn>. Auxiliary browsing contexts are always <span data-x="top-level browsing
-  context">top-level browsing contexts</span>.</p>
+  context</span> while their <span data-x="bc-container">container</span> is null. Such browsing
+  contexts are called <dfn data-x="auxiliary browsing context" data-lt="auxiliary browsing context"
+  data-export="">auxiliary browsing contexts</dfn>. Auxiliary browsing contexts are always <span
+  data-x="top-level browsing context">top-level browsing contexts</span>.</p>
 
   <p>The transitive closure of <span data-x="parent browsing context">parent browsing contexts</span>
   for a <span>browsing context</span> that is a <span>nested browsing context</span> gives the list
@@ -78663,13 +78678,14 @@ dictionary <dfn>DragEventInit</dfn> : <span>MouseEventInit</span> {
    <li><p>Return <var>list</var>.</p></li>
   </ol>
 
-  <p>A <code>Document</code> is said to be <dfn data-export="" data-dfn-for="Document">fully
-  active</dfn> when its <span data-x="concept-document-bc">browsing context</span> is non-null and
-  it is the <span>active document</span> of that <span>browsing context</span>, and either its <span
+  <p>A <code>Document</code> <var>d</var> is said to be <dfn data-export=""
+  data-dfn-for="Document">fully active</dfn> when <var>d</var>'s <span
+  data-x="concept-document-bc">browsing context</span> is non-null, <var>d</var>'s <span
+  data-x="concept-document-bc">browsing context</span>'s <span>active document</span> is
+  <var>d</var>, and either <var>d</var>'s <span
   data-x="concept-document-bc">browsing context</span> is a <span>top-level browsing context</span>,
-  or it has a <span>parent browsing context</span> and the <code>Document</code> <span
-  data-x="browsing context nested through">through which</span> it is <span data-x="nested browsing
-  context">nested</span> is itself <span>fully active</span>.</p>
+  or <var>d</var>'s <span data-x="bc-container-document">container document</span> is <span>fully
+  active</span>.</p>
 
   <p>Because they are associated with an element, <span data-x="child browsing context">child
   browsing contexts</span> are always tied to a specific <code>Document</code> in their <span>parent
@@ -78731,23 +78747,10 @@ dictionary <dfn>DragEventInit</dfn> : <span>MouseEventInit</span> {
    spec=NAVMODEL></p>
   </div>
 
-  <p>A <span>browsing context</span> that is a <span>nested browsing context</span> can be put into
-  a <dfn>delaying <code data-x="event-load">load</code> events mode</dfn>. This is used when it is
-  <span data-x="navigate">navigated</span>, to <span>delay the load event</span> of its
-  <span>browsing context container</span> before the new <code>Document</code> is created.</p>
-
-<!--(There's no current way for this to happen, since removing an iframe from a document discards its browsing context)
-  <p class="note">A <span>nested browsing context</span> can in some cases be taken out of its
-  <span>parent browsing context</span> (e.g. if an <code>iframe</code> element is removed from its
-  <code>Document</code>). In such a situation, the <span>nested browsing context</span> has no
-  <span>parent browsing context</span>, but it still has the same <span>browsing context
-  container</span> and is still <span data-x="browsing context nested through">nested through</span>
-  that element's <span>node document</span>. Such a <span>nested browsing context</span> is <em>not</em>
-  a <span>top-level browsing context</span>, and cannot contain <code>Document</code>s that are
-  <span>fully active</span>. Furthermore, if a <span>browsing context container</span> (such as an
-  <code>iframe</code>) is moved to another <code>Document</code>, then the <span>parent browsing
-  context</span> of its <span>nested browsing context</span> will change.</p>
--->
+  <p>A <span>child browsing context</span> can be put into a <dfn>delaying <code
+  data-x="event-load">load</code> events mode</dfn>. This is used when it is <span
+  data-x="navigate">navigated</span>, to <span>delay the load event</span> of its
+  <span data-x="bc-container">container</span> before the new <code>Document</code> is created.</p>
 
   <p>The <dfn>document family</dfn> of a <span>browsing context</span> consists of the union of all
   the <code>Document</code> objects in that <span>browsing context</span>'s <span>session
@@ -80441,6 +80444,13 @@ dictionary <dfn>WindowPostMessageOptions</dfn> : <span>PostMessageOptions</span>
 
    <li><p>If <var>browsingContext</var> is a <span>top-level browsing context</span>, then
    <span data-x="bcg remove">remove</span> <var>browsingContext</var>.</p></li>
+
+   <li>
+    <p>Set <var>browsingContext</var>'s <span data-x="bc-container">container</span> to null.</p>
+
+    <p class="note">This is a no-op if <var>browsingContext</var> is a <span>top-level browsing
+    context</span>.</p>
+   </li>
   </ol>
 
   <p>User agents may <span data-x="a browsing context is discarded">discard</span> <span
@@ -91580,18 +91590,18 @@ dictionary <dfn>PromiseRejectionEventInit</dfn> : <span>EventInit</span> {
       must be met:</p>
 
       <ul>
-       <li><p>Any <code>Document</code> <var>B</var> that is <span data-x="browsing context nested
-       through">nested through</span> a <code>Document</code> <var>A</var> must be listed after
-       <var>A</var> in the list.</p></li>
+       <li><p>Any <code>Document</code> <var>B</var> whose <span
+       data-x="concept-document-bc">browsing context</span>'s <span
+       data-x="bc-container-document">container document</span> is <var>A</var>, must be listed
+       after <var>A</var> in the list.</p></li>
 
        <li><p>If there are two documents <var>A</var> and <var>B</var> whose <span
-       data-x="concept-document-bc">browsing contexts</span> are both <span data-x="nested browsing
-       context">nested browsing contexts</span> and their <span data-x="browsing context
-       container">browsing context containers</span> are both elements in the same
-       <code>Document</code> <var>C</var>, then the order of <var>A</var> and <var>B</var> in the
-       list must match the relative <span>tree order</span> of their respective <span
-       data-x="browsing context container">browsing context containers</span> in
-       <var>C</var>.</p></li>
+       data-x="concept-document-bc">browsing contexts</span> are both <span data-x="child browsing
+       context">child browsing contexts</span> whose <span data-x="bc-container-document">container
+       documents</span> are <code>Document</code> <var>C</var>, then the order of <var>A</var> and
+       <var>B</var> in the list must match the <span>shadow-including tree order</span> of their
+       respective <span data-x="browsing context container">browsing context containers</span> in
+       <var>C</var>'s <span>node tree</span>.</p></li>
       </ul>
 
       <p>In the steps below that iterate over <var>docs</var>, each <code>Document</code> must be
@@ -103929,30 +103939,22 @@ dictionary <dfn>StorageEventInit</dfn> : <span>EventInit</span> {
    </li>
 
    <li>
-
     <p>If the <span>HTML parser</span> for which this algorithm is being run is associated with a
-    <code>Document</code> that is itself in a <span>nested browsing context</span>, run these
-    substeps:</p>
+    <code>Document</code> <var>d</var> whose <span data-x="concept-document-bc">browsing
+    context</span> is non-null and a <span>child browsing context</span>, then:</p>
 
     <ol>
-
-     <li><p>Let <var>new document</var> be the <code>Document</code> with which the
-     <span>HTML parser</span> is associated.</p></li>
-
-     <li><p>Let <var>parent document</var> be the <code>Document</code> <span
-     data-x="browsing context nested through">through which <var>new document</var> is
-     nested</span> (the <span>active document</span> of the <span>parent browsing context</span> of
-     <var>new document</var>).</p></li>
-
-     <li><p>If <var>parent document</var>'s <span>origin</span> is <span>same origin</span> with
-     <var>new document</var>'s <span>origin</span>, and <var>parent document</var>'s <span
-     data-x="document's character encoding">character encoding</span> is an <span>ASCII-compatible
-     encoding</span>, then return <var>parent document</var>'s <span data-x="document's character
-     encoding">character encoding</span>, with the <span
-     data-x="concept-encoding-confidence">confidence</span> <i>tentative</i>.</p></li>
-
+     <li><p>Let <var>parentDocument</var> be <var>d</var>'s <span
+     data-x="concept-document-bc">browsing context</span>'s <span
+     data-x="bc-container-document">container document</span>.</p></li>
+
+     <li><p>If <var>parentDocument</var>'s <span>origin</span> is <span>same origin</span> with
+     <var>d</var>'s <span>origin</span> and <var>parentDocument</var>'s <span data-x="document's
+     character encoding">character encoding</span> is an <span>ASCII-compatible encoding</span>,
+     then return <var>parentDocument</var>'s <span data-x="document's character encoding">character
+     encoding</span>, with the <span data-x="concept-encoding-confidence">confidence</span>
+     <i>tentative</i>.</p></li>
     </ol>
-
    </li>
 
    <li><p>Otherwise, if the user agent has information on the likely encoding for this page, e.g.