journey to savage planet sounds like it fits your criteria

Valheim and Raft are both fun with two people. Raft's a bit janky but more relaxed. Valheim can be relaxing or as hard as you want to make it (there are world settings you can change and plenty of mods), and although it's technically still in early access there's a ton of content.

My girlfriend and I have spent many fun hours playing Lethal Company. It's a real blast with an insanely high skill ceiling if that's your thing.

PlateUp! The better overcooked (this time, roguelike). Love this game. Might test your relationship a little though...

Sonic Racing Crossworlds. The bots are plenty tough on the hardest difficulty. But you can make them easy too.

GRIS

I know that you said multiplayer, but if I can be one more voice on single player games that you guys may enjoy playing in turns I strongly recommend GRIS. It is so beautiful and I think it suits itself well for shorter play sessions.

Me and my husband play this on emulator

https://en.wikipedia.org/wiki/X-Men_Legends

Something you might want to consider is that often boardgames nowadays have an electronic equivalent. Case in point, my best mate and myself recently played The Dresden Files over Steam.

I haven't seen anyone say Enshrouded yet. Im hosting a server on wine/linux for my group. Its like Valheim but with more direction like a quest log and lore and etc. Lots of good reccs on the thread already too.

I know its kinda crazy for me to.suggest this, but hear me out:

Hyrule Warriors Definitive Edition runs nearly perfectly in emulators on pretty modest hardware. Its not very difficult, but has a Games Journalist level Easy mode as well if thats needed. Its a Musou/Warriors game, so its basically mindless button mashing with the flavor of Zelda.

Its a splitscreen game, so you only have to have it set up on one machine. The game has a story mode and a bunch of challenge modes as well to keep things interesting. Wide range of upgradeable charaacters with different weapons that change up their playstyles. And a lot of unlockable costumes.

Downsides:

• Nintendo
• Have to use a controller (not a downside to me, but for sosme it is)
• Getting the game can be a little challenging if you don't know where to look
• Setting up the emulator can also be challenging if you don't know where to get the important parts
• Can get stale after really long sessions of play

Upsides:

• No account or extra launcher required, boot the emulator and play the game
• Most emulators have decent to great Linux compatibility
• Fully offline - no randos joining or server outages when internet drops
• Only two players can play, meaning nobody else can join after your partner, and Player 1 controls when Player 2 joins

The only issue could be if you aren't using a Nintendo controller, the buttons won't match up, but there might be a mod for that. I know there are input mods for other games.

Bokura, 2d puzzle platformer played with 2 players

It requires Steam, both players need to own the game, and two separate devices to play on (one for each player). Iirc networking goes through Steam, no way to selfhost.

Here is list of some games that I enjoyed playing with my wife:

One of my favorite recent games were: Ale and Tale Tavern and RV there yet.

Here is list of other game I have played and liked Farming sims: Stardew Valley Roots of Pacha Sun Haven T Action:

I do not know how well it fits your characteristics but Sea of Stars is a cool retro rpg you can play in coop.

I heard puzzle games and am legally obligated to shill Petal Crash (and it's upcoming sequel). It's a great accessible entry point into versus puzzles, and tbh it's practically the only good thing to happen to the genre in a decade or so.

Can also check out Panel Attack as a FOSS clone of Panel de Pon, and FightCade for emulating all kinds of classics with netplay.

If you want some retro, try Dungeon Siege. Works on Linux. I played this game when it came out and recently got back into it because I never finished it there first time. Really chill dungeon rpgish game. Easy mechanics, but I haven't tested how the multiplayer works.

One I haven't seen yet is Unrailed. It's a little bit of the chaos of overcooked, but not quite as stressful.

What you can do is take turns playing a single player game (if you are in person) such as the last of us. you take turns playing the game until you die etc. Since I assume you are more familiar with games, if it is your turn and you know that something cinematic or cool is going to happen, make sure to die beforehand so they get to experience it.

I mention this/these types of games cuz its a good couch game + you can make a shit ton of popcorn or pizza bites for the person whose currently watching.

Other than that, every recommendation here sounds solid!

Try emulating Kirby and the Forgotten Land using a Switch emulator.

I recommend avoiding people's recommendations for PC-only/indie games altogether. You will be lowering your standards just to get something that 'works' rather than something that's actually worth your time.