[3.13] gh-120838: Add a Note in the Docs About Expectations for Py_Fi…

…nalize() (gh-120852)

(cherry picked from commit 03fa2df, AKA gh-120839)

Co-authored-by: Eric Snow <ericsnowcurrently@gmail.com>

Doc/c-api/init.rst

@@ -396,9 +396,16 @@ Initializing and finalizing the interpreter
    :c:func:`Py_NewInterpreter` below) that were created and not yet destroyed since
    the last call to :c:func:`Py_Initialize`.  Ideally, this frees all memory
    allocated by the Python interpreter.  This is a no-op when called for a second
-   time (without calling :c:func:`Py_Initialize` again first).  Normally the
-   return value is ``0``.  If there were errors during finalization
-   (flushing buffered data), ``-1`` is returned.
+   time (without calling :c:func:`Py_Initialize` again first).
+
+   Since this is the reverse of :c:func:`Py_Initialize`, it should be called
+   in the same thread with the same interpreter active.  That means
+   the main thread and the main interpreter.
+   This should never be called while :c:func:`Py_RunMain` is running.
+
+   Normally the return value is ``0``.
+   If there were errors during finalization (flushing buffered data),
+   ``-1`` is returned.
 
    This function is provided for a number of reasons.  An embedding application
    might want to restart Python without having to restart the application itself.