Describe the project you are working on

A game using audio middleware (the unofficial FMOD integration)

Describe the problem or limitation you are having in your project

FMOD (and presumably other audio middleware) doesn't play its audio through the godot audio system, so the Game tab's mute button doesn't work.

Describe the feature / enhancement and how it helps to overcome the problem or limitation

Adding a way to access this button in the running game would allow middleware plugin developers to mute their audio backend if the button is toggled.

Describe how your proposal will work, with code, pseudo-code, mock-ups, and/or diagrams

Expose method / signal for getting the state of the mute button (Engine.is_debug_muted() -> bool signal Engine.debug_mute_toggled(state : bool) maybe?), all just returning false in release builds.

If this enhancement will not be used often, can it be worked around with a few lines of script?

Can't be implemented in script, requires private engine state.

Is there a reason why this should be core and not an add-on in the asset library?

Requires (currently) private engine state.