Momentary Stop push-down happens in yield to the idle time handler...

... So that ControlToolBar::StopPlaying now does nothing directly to the
buttons, and can be moved to another place with no dependency on ControlToolBar

src/ProjectAudioManager.h

@@ -43,6 +43,8 @@ public:
    // active
    bool Recording() const;
 
+   bool Stopping() const { return mStopping; }
+
    // Whether the last attempt to start recording requested appending to tracks
    bool Appending() const { return mAppending; }
    bool Looping() const { return mLooping; }
@@ -52,6 +54,7 @@ public:
    void SetAppending( bool value ) { mAppending = value; }
    void SetLooping( bool value ) { mLooping = value; }
    void SetCutting( bool value ) { mCutting = value; }
+   void SetStopping( bool value ) { mStopping = value; }
 
 private:
    // Audio IO callback methods
@@ -71,6 +74,7 @@ private:
    bool mAppending{ false };
    bool mLooping{ false };
    bool mCutting{ false };
+   bool mStopping{ false };
 };
 
 AudioIOStartStreamOptions DefaultPlayOptions( AudacityProject &project );

src/toolbars/ControlToolBar.cpp

@@ -808,10 +808,20 @@ void ControlToolBar::StopPlaying(bool stopStream /* = true*/)
    if (!CanStopAudioStream())
       return;
 
-   mStop->PushDown();
-
    auto gAudioIO = AudioIO::Get();
 
+   auto cleanup = finally( [&]{
+      projectAudioManager.SetStopping( false );
+   } );
+
+   if (stopStream && gAudioIO->IsBusy()) {
+      // flag that we are stopping
+      projectAudioManager.SetStopping( true );
+      // Allow UI to update for that
+      while( wxTheApp->ProcessIdle() )
+         ;
+   }
+
    if(stopStream)
       gAudioIO->StopStream();
 
@@ -1296,8 +1306,11 @@ void ControlToolBar::OnIdle(wxIdleEvent & event)
       );
    }
 
-   // push-downs of the stop button are only momentary and always pop up now
-   mStop->PopUp();
+   if ( projectAudioManager.Stopping() )
+      mStop->PushDown();
+   else
+      // push-downs of the stop button are only momentary and always pop up now
+      mStop->PopUp();
    
    UpdateStatusBar();
    EnableDisableButtons();