The new Shadowrun games are excellent! VERY low-power CRPGs with a nice aesthetic.
Fallout 1 and 2 are good bets, too. They’re old enough that you pretty much have to just rely on your touchpads, but if you don’t mind that they’re fantastic CRPGs that run shockingly well on the Deck. For that matter, Fallout 3, New Vegas, and 4 all run really well.
Black Ops 3 has a splitscreen mode, primarily for zombies but I’m pretty sure it works for multiplayer and campaign too. Ideally you’d want to get it with zombies chronicles because that’ll give you a bunch of classic maps, but even with absolutely zero DLC you can get a TON of custom maps.
I BELIEVE Portal 2 has splitscreen support on PC? Picking up the new Lego Star Wars is a good time, too, and Left 4 Dead 2 has a couple of relatively easy-to-install mods that enable a splitscreen mode too.
Depends on how long I anticipate staying in sleep mode. If I’m gonna be putting the thing away for more than, say, 30 minutes? I’ll put in the effort to find a safe spot to save and I’ll close the game, but anything less and I’ll just suspend it.