WiFi might work but I don’t think BT or USB could. KVM like you say it probably the way. https://looking-glass.io/ seems promising.

I’ve been using https://github.com/JacKeTUs/linux-steering-wheels for reference.

You can add Nested Desktop from the application launcher to Steam to get a near complete desktop experience in game mode. It’s very convenient for using Konsole and other desktop apps. I use it a lot.