I ve seen nucleuscoop to be a reasonable splitscreen manager for theese kind of situations
Here it is a link related to this particular subject: https://www.reddit.com/r/localmultiplayergames/comments/bxyx7a/outward_4_player_local_splitscreen_coop/
I would also reccommend setting up Extended Quickslot
While if I'm understandig this correctly the problem of both games being affected by the same keyboard would still exist maybe you can differentiate the keypresses bound for player one and those only affecting player two, I never tried it myself.
Let me know if you find out, have a good one.