Valheim if you want action, building, or relaxing things like chopping wood and breaking rocks. In more of a boardgame direction, there's Sagrada, Dominion, Takenoko, Carcassonne, Istanbul, or Splendor. All of which I have played on my SD multiplayer. Usually these games end up using the left stick and the right track pad as the mouse, which seems to work fine for me.
Stardew Valley, possibly factorio (don't k ow about the custom control scheme, the game is great), trackmania, borderlands 2, plate up, gang beasts, and the jackbox party games.
Ultimate Chicken Horse has quickly become the goto-local-multiplayer in my group.
The game design is so devilishly elegant: you co-create 2D jump&run levels. Together you want to make them so easy that at least one player can finish the level (and get points), but also hard enough that not all of the group get through (no one gets points).
It’s great. Will most likely be on sale. Don’t sleep on it!
The Master Chief collection. Runs great, and has both co-op and competitive multiplayer. Not on sale ATM but I bought it for $10 not too long ago.
Curveball suggestion: Phantasy Star Online Blue Burst. I loved PSO back in the day and it’s amazing to me that I can install it on the Deck through Lutris.
It was something like 18 years ago I spent my entire summer vacation playing PSO, went to bed at 8am and woke up in the evening so I could play with US people as there weren't enough EU players on schthack.
Guess it's time to spin it up once more for old times sake.