Kevin04: Coop technically works, in general. I didn't experience any problems actually establishing a session, i. e. joining and staying in a game worked fine.
However, just as a warning, the coop experience once playing was abysmal for us. It's all pretty fine for the host, except that it looks like the coop partner lags a lot. The partner however has to deal with a lot of lag and sync problems, including being teleported back to previous positions (in extreme cases even 10 seconds of moving or more are lost, multiple times), the game world not updating properly (breakable walls stay intact after breaking, eaten orange goos are still there, grappling seeds can't be placed, ...), the proton tether being very unreliable with janky camera movement so grappling is a real risk or all kinds of stuff just not working for the partner at all so you have to let the host do it. We got surprised with new ways the game breaks for the coop player right until the very end. It's completely inconsistent - you can still finish the game that way, even 100% as we did, but it's a frustrating.
I have no idea if it's an isolated problem for us (four people in three different households). Apparently it works fine on Steam, because we had another pair of players there. Swapping hosts didn't help. It's definitely an odd one out for us, we play other games too and they work fine, even over Galaxy.
EDIT: "breakable walls stay broken" made no sense, also fixed some minor grammatical errors