I think you’ve misunderstood again.

In my call, I left the mic open by default, and configured a key as push-to-mute.
In the game, I left the mic muted by default, and configured the same key as push-to-talk.

This way, I could speak on the call or in the game, but never both at once, and the my was not open by default in the game.

Edit: Oh, I think I figured out what your first sentence was supposed to mean. I think you want not only to choose between two voice chats (a game and a call) when talking, but also be muted in both by default so other sounds in the room won’t be heard by anyone. Yes?