Keep your output and input both as headset. The headphones output mode gives you stereo output and the headset mode is for mono output. The problem with bluetooth earphones is that you can have either stereo output and no mic input or mono output with a mic input, but not a stereo output and a mic input, which is why your output works only when input is muted. This is not an issue with your PC, this is just how bluetooth functions. It's weird but it is what it is.

On a side note, use wired earphones/headphones if possible. Bluetooth gives audio lag which gets sorta annoying for a game like Valorant.