Synchronize both pause modes: top-right "Pause Running Project" button and game view "Suspend/Resume Embedded Project" button

[hsandt]

Currently, the top-right "Pause Running Project" and game view "Suspend/Resume Embedded Project" buttons are completely unrelated. I can press one without affecting the other, which may lead to confusing states such as having the game paused but being unable to press the Next Frame button in the game view:

Game is globally paused...

but game view doesn't recognize it.

Reversely, I can pause the game view...

but not the global view

Is there a design or technical reason for this? Any particular advantage to having two different layers of pause?
If this can't be helped, could be UI be made clearer to distinguish both pause buttons?

Otherwise, my proposal is to synchronize both pause modes. Clicking on one button would toggle the other, and when in global pause you could Advance to Next Frame. This would also avoid having two shortcuts for Pause/Suspend/Resume.

[hsandt]

Related: #11595 (it's about adding Close/Quit button to game window, but which would be a duplicate button but doing the same thing as the existing one)

[Meorge]

I don't have a link handy, but I recall this has been discussed before. In 4.6, the buttons use different icons and have tooltips that distinguish their behaviors a bit more:

[hsandt]

Ah yes, that makes sense. I see how the Debugger slightly changes when pausing manually. If godotengine/godot#117133 is fixed we may even be able to evaluate expression on project-level pause (as opposed to tree suspend).