That would apply for older HMDs and mostly to the controllers but completely moot with Steam letting you change bindings, any modern HMD is compatible with any and all Steam VR games (real games not abandoned demos). As for your question, yes they do work with the Quest 2.

Btw, claiming your PC is brand new says nothing at all, there's still new low-end hw being manufactured...

They work fine streamed to a Quest 2.
The settings require a bit of tweaking to avoid getting sick.
VR mods make them a LOT easier to play in and a lot more fun to play.
The only games that "don't work on certain headsets" nowadays are really old-pre-Steam VR games that were coded directly for one single headset. Or ones with goofy-ass controls. The Quest 2 is the most common headset there is on the Steam Hardware Survey.
Steam VR/Open VR is what makes all this shit work out fairly easily.
The games you want to avoid buying is any VR title by IF. You know, the company that produces those JRPGs with the word "Neptunia" in the title? They were originally coded for the PSVR. Which the Bethesda titles were as well.
The problem with the IF titles is that the publisher gave the firm they contracted to do the PC VR ports VERY specific (and stupid!) instructions. "Make these games compatible with the Oculus Rift CV1 and the HTC Vive." Those were the two most-popular headsets on PCs back then. They coded directly to the headsets, not through Steam VR/Open VR. So even if you had an Oculus Rift S or a later HTC headset, none of those games work right on them.
This was a very rare thing, and the publishers annoyingly kept on selling these titles (and bundling them) for several years. Because they don't know how to code VR and don't appear to be interested into putting money into them to make them work with open standards, they're kind of abandonware that they somehow keep on selling. Are there a handful of similarly-coded games on Steam? Probably, but most have been bombarded with negative reviews and they have the dead-giveaway date of XX/XX/2015 or so on them.
With Bethesda's games, you just need to follow a guide on Steam to get the comfort settings at a point to avoid getting the queasies. Modding them makes them work a lot better.