My partner and I occasionally play games together, but they pretty much only play word puzzle games on their own. I'm not very good at word games though, and they don't have very good spatial skills, so we frequently find ourselves mismatched. We have a switch and a single decent gaming pc, and a pretty old laptop.
The biggest hit for us has been Baba is You because it is slow paced, and combines words and logic and spatial reasoning. Our biggest problem was that its not actually coop, so we would just alternate who played, which can disengage the other person. My partner also thought its aesthetic is cute.
Our next positive example is probably Snipperclips is also a pretty slow paced puzzler, is mostly spatial skills, but we could play at the same time. They also liked how interactive the avatars are, and particularly snipping my avatar up.
The first miss is overcooked, it was a bit too chaotic, and my partner felt a little lost and uncoordinated. They don't remember it super well, so we might retry this one at some point if they feel more at home playing video games.
The other miss is Mario Kart, which they liked when we played with 4 player, but not just the 2 of us. I'm significantly better at Mario Kart, and they are pretty competitive. If they get more into games they might be willing to put in some time improving, but not so much right now.
Our worst miss was probably Tricky Towers, I'm decently good at regular Tetris, so I can do okay out of the box at physics based Tetris, but there was too much happening to fast for my partner. Combine that with it the competitive aspect and they didn't enjoy this one at all.
The games they most fondly remember from childhood are Dance Dance Revolution and Guitar Hero, though we have downstairs neighbors under part of our apartment and no dance pad or guitars, SSX Tricky, and the Lord of the Rings movie tie in games.
They think they'd enjoy a game that does movement as input like ddr or guitar hero but is maybe less bouncy, and are open to action games, or games with a story, but they should be easier to control and not be too chaotic. Cute aesthetics and cats are a plus.
Thanks!
Edit: Everybody gave great recommendations! We picked up It takes two and pizza possum. Just finished the first chapter of it takes two and we had a blast, and I might even be able to get another game night in this weekend if we can be on top of chores. I'll keep checking in this thread for more ideas for future games to try! Thanks again!
Lego games like Lego Starwars has already been mentioned and I will second those (especially the newer ones that have split screen).
Divinity Original Sin is also great.
Honestly most games I can think of have already been mentioned and those who have not seem like they might not be that great of an option since it seems your partner isn't normally into gaming. (RTS in particular might be too hard)
But I will suggest some anyway just in case
Starcraft 2 has free online multiplayer which includes a COOP vs AI mode.
There's also a 2 player campaign adaption of Warcraft 3's normally single player campaign. Although it might only be available for pre-Reforged.
Also I didn't know about it before now, I googled it just in case, but apparently SC2 also has COOP mods for its campaigns.
You mentioned having a Switch so I will recommend Advance Wars Reboot and Wargroove 1 & 2, although there are no COOP campaigns but you can play multiplayer maps.
Besides Advance Wars Reboot Camp on Switch (or the originals for Gameboy, which you could play with emulator), there's also an online fan site called Advance Wars By Web where you can play advance wars in the web browser, although there's no single player.
Wargroove is also on Steam and besides the campaign and regular game itself there are puzzles.
And speaking of Puzzles, card games tend to have Puzzles. I haven't actually played Magic, Yu Gi Oh, etc. so I can't say for sure whether they have any, but there's puzzles in Faeria. (I would've recommended Might and Magic Duel of Champions, it had some great puzzles, but Ubisoft shut that game down many years ago)
Also StarCraft 2 can be modded with MassRecall so you can go through the SC1 campaigns, more than just SC and Broodwars, in the SC2 engine, which makes them a bit easier and more satisfying. I think that would allow you to do co-op on the original single player campaigns.