Game Recommendations for LDRs

I enjoyed playing Fall Guys. Rounds can be short, and while you said you don't like jump puzzles, it's mostly not a puzzle game. It's very casual and low stress IMO. Can play as duos, where you're both on the same team, or individually. There are also co-op modes with no PVP.

he refuses to play stardew valley because it has a rigid calendar and i personally find sdv really stressful

Good call then, in (unmodded) multiplayer the clock never stops, as opposed to single-player (arcade machine games, fishing, or the time-slowing effect of the mines)

Good old Borderlands 2?
Some gun and run games, like Guns, Gore and Cannoli?
Adventure Pals?
Antihero can be an interesting "boardgame" that you can play against eachother, and as I heard it even works in asynchronous ways - so you can make your move in the morning, your partner theirs 3 hours later, and you can check it in the afternoon
Assault Android Cactus is a fantastic twin stick shooter / bullethell game. Also almost anything from 2tons ltd, like JYDGE, Neon Chrome, etc
Death Road to Canada looks pretty fun as well
Trine series!
Good old Worms, be it Armageddon, Reloaded, and idk, there are too many

Human Fall Flat may be a mixed bag, it has some jump puzzley-things, but the whole game is just... not serious. You can often solve the levels in different ways, it's made to be a semi-silly multiplayer game.

Hunted: The Demon’s Forge™ fairly much the best 2-player coop game I've played, as it's fully designed for duo coop play like rarely any other (and for why not great when played alone).

Project Eden a bit older with dated graphics, but fantastic cooparative design, while supporting up to 4 players, it's still excellent with 2 as well.

Obscure if horror themed games are your thing, that's a neat one to play, not as good as the other 2 but still worth a round. It has like 7 different ending cinematics depending how you fare.

Not sure if this would your cup of tea, but maybe you'll like The Dark Picture Anthology games. Granted I've only played Man Of Medan and House of Ashes, but it was a lot of fun playing with my gf.
Its a horror series that plays much like an interactive movie in some parts, while on the other you can move in an area, think of it like Telltale games.
Another game that I highly recommend is Death Road to Canada, its a lot of fun, plus it has some hilarious characters you can find. The only problem is that I think you can only play couch coop, but we have steam remote play so that could fix it.
Children of Morta could work too, if you enjoy roguelikes .
Edit : Project Zomboid is another game you might wanna try, if you are into post apocalypses zombie survival games.
Not many suggestions from me, but hope those would help you. Good vibes from the Commissar :D

For The King II.

If you like Risk of Rain 2, I recommend Gunfire Reborn

try rayman legends maybe !!
it takes two
unravel two
trine games

And ldr would be?

if you'd like something cozy: ibb & obb
i know it's unlike anything you mentioned but it's memorable for me from when i was in a LDR as well

Maybe Biped? Brotato has added coop recently... Maybe virtual board games like carcassonne?

Iif you use TTS already, try (if you have not done so) some legacy/campaign game, e.g. Pandemic Legacy scripted or Gloomhaven.

Pool Panic

Don't play much co-op myself, but Sackboy is a fun platformer and has co-op mode.

Not sure if any of these would be your cup of tea, but I thought them worth suggesting as they are games my SO and I have enjoyed playing:
ContractVille
Farming Simulator 22
Medieval Dynasty
Sengoku Dynasty
Green Hell
Ranch Sim
Palworld
Escape Simulator
Planet Crafter
the "We Were Here" series
Icarus
Generation Zero
theHunter: Call of the Wild
Castle Crashers
Space Engineers
Wurm Unlimited
Saint's Row 2

These are in no particular order :P
I hope this helps, and you find more things to enjoy together :)

Keep Talking and Nobody Explodes

Some of these are definitely not low energy... but:

• 100% Orange Juice
• Earth Defense Force 4.1, 5 & 6
• Orcs Must Die 2 & 3
• Diablo 2
• Grim Dawn
• Remnant 1 & 2
• Roboquest
• Gunfire Reborn

lots of good recs here. i may be repeating some, but they're some good ones i had in mind..

we were here series - first release is free if you wanna get an idea of what to expect. the sequels are more of the same (i mean that in the best way possible) and the price of the games general reflect the amount of content.

gunfire reborn - played this a bit with a buddy on game pass before they removed it and i unfortunately don't own it on steam. like the description says, it's an fps roguelite with rpg mechanics.

deep rock galactic - kind of in the same vein as gunfire reborn. fps, roguelite, rpg elements. one of steam's highest rated and most popular games for a good reason.

dark pictures anthology series - a little more niche here, but if you're into supermassive's movie-like type of "choose your own adventure" games then these are pretty decent. only one person needs to own a copy and the other can play for free with a friend pass.

escape simulator - really fun escape room style game. comes with several dozen levels, but there are hundreds more you can download for free via steam workshop.

Kingdom Two Crowns

What about something like PowerWash Simulator?

Or The Planet Crafter.

Trine series perhaps, assuming that doesn't fall into the Jump Puzzler category? :)

Don't recommend It Takes Two, not my type of game and I HATE jump puzzles lol.

I was actually coming to say "not recommending It Takes Two" ;)

Lego games are always fun and take very little time setting up. Lord of the Rings is the best in my opinion but the Skywalker Saga is also brilliant.
Other recommendations for games I played with my gf (also in a semi LDR):
The Deadly Tower of Monsters (honestly hilarious and a lot of fun)
No Man's Sky (improved a lot although you need two copies of the game)
Spiritfarer

Sending you good vibes