Why an additional button? In my games you simply move the volume slider to 0. Additionally (because I e.g. play actual baroque music in my "Building Baroque" game) I have button to display the title of the piece that's currently playing. BTW: There is a lot of public domain classical music if that would be something for your game.
If you have a mute button, you can have a remembered audio level. Turning sound on again will reset to that level, instead of the user trying yet again to find the right setting. 100% is not always right.
People that do change their audio settings will also be the ones that will expect a certain quality of life here. It is basic UI design, or it should be, along with a lot of other things, that new developers seem to forget when making a game. Same for engines. You seem to use Unity. Why is this not an out of the box standard feature?
