For your regular PC, you can install a gaming-focused distribution like Bazzite to get everything sorted out automatically.
I assert that most people who're happy running Linux on their desktop (for games or productivity or development) do not overlap much with the people who're happy to take kernel patches from UbiFuckingSoft. And this includes those people who're willing to take closed-source NVIDIA drivers.
That way Linux gamers can still play with other Linux gamers if they want (and cheaters).
Not an ideal situation but probably better than nothing.
Segregating into two pools: Windows-verified, or Linux-unverified, would probably not work for Linux users either. It'd be the same problem (on a smaller scale) as not including kernel anticheat in Windows. No fun for the non-cheaters.
I'm not a gamer though, so I may be missing important details.
A good rule of thumb is that single player games generally just™ work and that older games generally just™ work.
"Mainstream" is maybe too hefty, the amount of Linux users (including SteamDeck) who participate in the Steam surveys are still in the single digit if I remember correctly. Most gamers today still use Windows, even though Valve made great strides with Proton.
Age of empires will be okay.
[0]: https://www.protondb.com/explore [1]: https://areweanticheatyet.com/