Well, mixers aren't cheap. The Logitech mixer is not what you're really going to want. There are very low latency mixer software for pc, https://www.vb-audio.com/Voicemeeter/, for example, would let you mix game input with discord on the pc, but I don't know how much latency you'd be looking at. You can try it and see if it does the trick.
https://www.guitarcenter.com/Nady/MM-242-4-Channel-Mini-Mixer.gc should do the trick.