Tweak async iterator algorithms

Make both the "async iterator initialization steps" and the "get the next iteration result" take two arguments: the instance, and the async iterator. This ends up being more ergonomic than using the "current state" concept.

index.bs

@@ -4299,19 +4299,17 @@ and {{@@asyncIterator}} properties on its [=interface prototype object=].
 
 Prose accompanying an [=interface=] with an [=asynchronously iterable declaration=] must define a
 <dfn id="dfn-get-the-next-iteration-result">get the next iteration result</dfn> algorithm.
-This algorithm receives a <b>[=this=]</b> value, which is an instance of the [=interface=] that it
-is defined for, and the <dfn export>current state</dfn>.
+This algorithm receives the instance of the [=interface=] that is being iterated, as well as the
+async iterator itself (which can be useful for storing state).
 It must return a {{Promise}} that either resolves with undefined – to signal the end of the
-iteration – or a tuple with three elements:
+iteration – or a tuple with two elements:
 
 1.  a value of the first type given in the declaration;
-1.  a value of the second type given in the declaration;
-1.  an opaque value that is passed back to the next invocation of the algorithm as the
-    <b>[=current state=]</b>.
+1.  a value of the second type given in the declaration.
 
 The prose may also define <dfn>asynchronous iterator initialization steps</dfn> for the
 [=interface=] with an [=asynchronously iterable declaration=], which would then be called with the
-newly created iterator object.
+instance of the [=interface=] being iterated, as well as the newly created iterator object.
 
 [=Interfaces=] with an [=asynchronously iterable declaration=] must not have any
 [=interface members=] named "<code>entries</code>", "<code>keys</code>", or "<code>values</code>",
@@ -4341,26 +4339,32 @@ or have any [=inherited interfaces=] that have [=interface members=] with these
 
     <blockquote>
 
-        To [=get the next iteration result=] for <code class="idl">SessionManager</code>, run the
-        following steps:
+        The [=async iterator initialization steps=] for a <code class="idl">SessionManager</code>
+        async iterator |iterator| are:
+
+        1. Set |iterator|'s current state to "not yet started".
+
+        To [=get the next iteration result=] for a <code class="idl">SessionManager</code>
+        |manager| and its async iterator |iterator|:
 
         1.  Let |promise| be a new promise.
         1.  Let |key| be the following value, if it exists, or null otherwise:
             <dl class="switch">
-                  :  If <b>current state</b> is "not yet started"
-                  :: the smallest username in <b>this</b>'s open sessions, in lexicographical order
+                  :  If |iterator|'s current state is "not yet started"
+                  :: the smallest username in |manager|'s open sessions, in lexicographical order
 
                   :  Otherwise
-                  :: the smallest username in <b>this</b>'s open sessions that is greater than
-                     <b>current state</b>, in lexicographical order
+                  :: the smallest username in |manager|'s open sessions that is greater than
+                     |iterator|'s current state, in lexicographical order
             </dl>
 
-            Note: <b>current state</b> might no longer be present in the open sessions.
+            Note: |iterator|'s current state might no longer be present in the open sessions.
         1.  If |key| is null, then:
             1.  Resolve |promise| with undefined.
         1.  Otherwise:
             1.  Let |session| be the <code class="idl">Session</code> object corresponding to |key|.
-            1.  Resolve |promise| with (|username|, |session|, |username|).
+            1.  Resolve |promise| with (|username|, |session|).
+            1.  Set |iterator|'s current state to |username|.
         1.  Return |promise|.
 
     </blockquote>