Specify which event loop to use for posting messages

Closes #4653.

source

@@ -98436,13 +98436,6 @@ dictionary <dfn>CloseEventInit</dfn> : <span>EventInit</span> {
   <p class="note">This API <a href="#fingerprint-postMessage">has some privacy implications</a> that
   might not be immediately obvious.</p>
 
-  <div w-nodev>
-
-  <p>The <span>task source</span> for the <span data-x="concept-task">tasks</span> in
-  <span>cross-document messaging</span> is the <dfn>posted message task source</dfn>.</p>
-
-  </div>
-
 
   <h4>Introduction</h4>
 
@@ -98634,7 +98627,8 @@ function receiver(e) {
    any exceptions.</p></li>
 
    <li>
-    <p><span>Queue a task</span> on the <span>posted message task source</span> to run the
+    <p><span>Queue a task</span> on the <dfn>posted message task source</dfn> of
+    <var>targetWindow</var>'s <span>relevant agent</span>'s <span>event loop</span> to run the
     following steps:</p>
 
     <ol>
@@ -99480,7 +99474,12 @@ interface <dfn>BroadcastChannel</dfn> : <span>EventTarget</span> {
 
    <li>
     <p>For each <code>BroadcastChannel</code> object <var>destination</var> in
-    <var>destinations</var>, <span>queue a task</span> that runs the following steps:</p>
+    <var>destinations</var>, <span>queue a task</span> on the <span>DOM manipulation task
+    source</span> of <var>destination</var>'s <span>relevant agent</span>'s <span>event loop</span>
+    that runs the following steps. If that event loop is a <span>window event loop</span>, then the
+    <span data-x="concept-task">task</span>'s <span data-x="concept-task-document">document</span>
+    must be set to <var>destination</var>'s <span><code>BroadcastChannel</code> settings
+    object</span>'s <span>responsible document</span>.</p>
 
     <ol>
      <li><p>Let <var>targetRealm</var> be <var>destination</var>'s <span
@@ -99506,13 +99505,6 @@ interface <dfn>BroadcastChannel</dfn> : <span>EventTarget</span> {
      <var>sourceSettings</var>'s <span
      data-x="concept-settings-object-origin">origin</span>.</p></li>
     </ol>
-
-    <p>The <span data-x="concept-task">tasks</span> must use the <span>DOM manipulation task
-    source</span>, and, for those where the <span>event loop</span> specified by the target
-    <code>BroadcastChannel</code> object's <span><code>BroadcastChannel</code> settings
-    object</span> is a <span>window event loop</span>, must be associated with the <span>responsible
-    document</span> specified by that target <code>BroadcastChannel</code> object's
-    <span><code>BroadcastChannel</code> settings object</span>.</p>
    </li>
   </ol>