I've already got a pretty large library, so I'll give some recommendations (mostly older as haven't had much time of late). All PCVR as I prefer buying on Steam:

• Synthriders - rhythm game like beat saber but more dance focused

• Dirt Rally 2.0 - not sure what the status of sim racing on Linux (and the Frame currently) but a great experience if you're at all into racing

  • Automobilista 2 - similar quality but track instead of rally-focused

• Doom 3 Fully Possessed Mod - Doom 3 mod. I never really enjoyed the original game but in VR it's a lot of fun (and scary). Looks like the github repo has gone, so not sure where to find it today

• Eleven Table Tennis - Just what it appears to be, a nice table tennis again with somewhat realistic physics. Suprisingly fun.

• Half-Life 2: VR Mod - For when you've played Alyx to death and want something similar. A greater challenge as well since it wasn't designed as an intro to VR.

• Ragnarock - Another rhythm game that has a kind of viking drumming motif with a more rock/metal focused soundtrack

• Sniper Elite VR - A bit janky but feels like an oldschool WW2 game but in VR. Maps are a lot smaller than the mainline series though, likely due to standalone limitations.

• The Walking Dead: Saints & Sinners - This one has had controller issues with the open source Linux stack, but hopefully it will work well with the Frame. Semi-open world survival horror game with fun combat being the main draw. There's also a sequel/DLC but I haven't gotten to it yet.

• Crysis VR - The original Crysis in VR. The game in flat never really grabbed me, but is a lot more compelling as a VR game (although I'm a bit more prone to nausea with this one). See: https://crysis.vrmods.eu/

• UEVR mods - A bunch of games with unreal engine support this. A bit of a pain to setup and the quality of the experience varies, but opens up a lot of conventional games. See: https://uevr-profiles.com/

EDIT: I also suggest digging into the Steam Workshop mods for Alyx. There's a lot of good content there, and you get the fantastic Alyx engine and gunplay.

EDIT 2: I'll throw in a recommendation for this bundle: https://www.digiphile.co/collections/vr-games-showcase-the-new-essentials as it looks to have some well regarded games (Into the Radius 2 and Convrgence in particular)