In this case, two headsets would probably be the best solution. The closer a microphone is to the mouth, the less ambient noise it will pick up.

It is a condenser microphone, which picks up sounds in front of it better than those behind it, but at this distance it is still likely that both signals would be picked up.

In Discord, the minimum volume for enabling the microphone can be increased manually so that quieter noises no longer (always) trigger this - you could play around with this and see if the problem can be reduced or resolved.

If that doesn't help, you would have to look for dynamic (non-condenser) microphones (with which I unfortunately have no experience).

So I game without headphones and my colleagues can't hear the sounds of the games. Not sure if different voices could still be a problem.