If not for the fact you said one's on an Xbox, for a co-op experience I'd recommend Helldivers 2. However, a similar game to HD2 is Deep Rock Galactic, and it's on Xbox as well as PC. Fantastic co-op shooter with some very funny humor, much like HD2 you can tell a lot of love went into the game; and much like HD2 the developers actually give a shit about it and their community. Since you said you don't have a load of screen time, you should know a full mission is usually about 20-30 minutes.

For a PVP experience, you said you have two brothers -- three is actually the perfect number if you wanted to get Sniper Elite 5 and play through the campaign with Axis Invasion enabled, you can invite one to play co-op and for the other, you can invite a specific invader. Two players would be playing as allied snipers infiltrating various locations in France and taking out Nazis, and the third would be an elite German sniper hunting them. It's supremely fun to hunt people (as well as be "hunted" -- though with two players you can really flip that on its head). And a mission in SE5, depending on how you play, can either take as short as 15 minutes or as long as 45 minutes, though probably on the longer end if you're doing invasion -- you do not play it like COD if you actually want to survive against a hunter.

Both of those have crossplay and should work on a Steam Deck, as well; although I've noticed Sniper Elite 5's anti-cheat, when run through Proton on Linux, doesn't like the game being installed on an external drive and won't let you play online if it's not running on the same drive the OS is installed on, and I imagine that'd probably extend to SD cards. So, if you go for SE5, make sure that brother installs it to the Deck's internal storage or they might run into trouble.