Some quick thoughts on every game I've tried so far:
Flawless out of the box
Not much to say about these - they just work and perform well.
Civilization VI
Dark Souls Remastered
F1 2021
Fallout 4
Kingdom Come: Deliverance
Stardew Valley
Good
Battle Brothers - Great after some tweaks to the controls. Well suited to the deck and could be a huge timesink.
Fallout 2 - It's Fallout 2. On a handheld. And it damn well works! What a time to be alive.
Mass Effect Legendary Edition - Very excited about this as it works as well as I'd hoped. Only downgraded from Flawless due to the faff of Origin, but it's not an issue once set up.
Might and Magic X - Slight pain in getting Ubisoft Connect working and some control mapping required, but it runs nicely and is surprisingly easy on the battery.
Pillars of Eternity - Aside from some control changes for preference, works great.
Red Dead Redemption 2 - Would be in Flawless if not for the fact that after changing some graphics settings, it crashed and wouldn't restart, so I had to reinstall it. I think the mistake was changing it to DirectX12. Oh, and the Rockstar Social Club should be cast into the sea. Otherwise it runs great.
Tomb Raider - I can't remember exactly what the problem was, but there was a problem. Nothing huge, and it's now running fine.
Reasonable
Arcanum - Got it working! It needed an earlier version of Proton and now it works, which frankly astounds me given how flaky it is on my main gaming PC.
Crusader Kings 3 - Good in terms of performance; a bit clunky with controls but totally playable. UI scaling makes text readable. Probably just needs some control tweaks for preference.
Dragon Age: Origins - I'm tempted to put this in the Good category because now that I've got it working and configured properly, it's fantastic and I'm genuinely surprised how well it works with the controls. But getting to this point was a straight up nightmare. The low point was finally getting into the game only to find that dropdowns in the options menus didn't work, which meant I had to hunt down the virtual Windows documents folder so I could manually text-edit the config file as required. Would have been significantly easier if I'd bothered to plug in a mouse and keyboard.
Jedi: Fallen Order - A pain to set up initially due to Origin, but it also runs quite poorly even on the lowest settings, getting about 40fps while absolutely hammering the battery. It's fine and absolutely playable, but I feel like it should be getting better performance.
XCOM-2 - It works, but the controls are a bit weird and don't seem to map as intended. I've played it on Xbox before and it works fine with a controller, so I think it must be some setting that needs changing to make it recognise pad controls rather than mouse/keyboard controls in-game.
Bad
Baldur's Gate 2 (ehanced edition) - Strangely unresponsive and has some strange stuttering issues with visual effects like spells, which I can't account for given how old it is. A shame, as it isn't really playable in this state.
Rimworld - To be honest, I didn't expect this to do well. As much as I love the game, it's not well suited to the Deck at all. The controls are just too fiddly and text is tricky to read. I've left it installed as it should work just fine on an external monitor with a mouse and keyboard.
TIE Fighter - I had to try it! Sadly it doesn't work as it errors saying I need to plug in a joystick.
I expect there's a workaround but I'm yet to find it.
Wasteland 2 - The controls don't seem to work, even after manually setting them. The trackpads in particular do nothing, which is a bad for a game requiring mouse control. I've read that it's possible with some messing around but I've not got round to that yet. Has potential to be great on Deck, so it's a shame that it's unplayable by default.