On Samsung phones Samsung Gamelauncher Gaming Hub gives you the option to mute all game audio, but I’m afraid this is a Samsung exclusive feature.
Another feature I have on my Galaxy S10 is the ability to set different outputs for apps, ie. “bad sounds” from some app to phone speakers (which are muted), and the rest to my Bluetooth headphones.
On my phone this feature is called “Separate app sound” and is located in Settings > Sounds and vibration > Separate app sound. It might also be a Samsung exclusive though.
Edit: I have yet another, sadly probably Samsung exclusive, solution. Samsung Sound Assistant let’s you set a different volume for each app (like Windows volume mixer).