GOG absolutely does offer native Linux games.
That’s why people seem to recommend Lutris or some other alternatives to access the actual library.
I’ve had a really mixed experience with GoG on Lutris and Heroic - both on Pop and the Steam Deck. I often struggle to get things running. It requires just that little bit more knowledge of what’s happening under the hood than Steam/Proton does, and I often just give up. My library is mostly in Steam anyway. Honestly, EmuDeck has been easier for me to get uo and running than either Heroic or Lutris.
And both Nvidia and AMD have native control software (GeForce Experience and Adrenalin) that bundles a bunch of nice stuff like underclocking, recording, noise suppression, per-game profiles, frame limiter, etc;
On Linux you have GreenWithEnvy and CoreCTRL, but neither are as nice or have even half the features.
Every time I’ve tried it, it has just seemed slow, even on reasonably powerful PCs.
My budget gaming PC is still on Windows and RTSS is a lifesaver: I couldn't stream or record some games with my Intel Arc A580 otherwise, since titles that use DX11 or older rendering technologies typically have worse performance than the more recent ones, ergo I have to stream/record at 30 and cap the framerate anywhere between 30-60 depending on the title, otherwise things get unstable.
Of course, it's not ideal, but is at least workable. A bit odd that the card struggles with games like Ghost Recon Wildlands (DX11, 2017), but not Ghost Recon Breakpoint (Vulkan, 2019) or ones that use DX12 etc. Either that, or when there's a title that's badly coded and doesn't lock framerate properly to the screen refresh rate.
Aside from that, around 90% of the 500ish Steam games I have would actually run on Linux (various indie titles, mostly), at least according to ProtonDB: https://www.protondb.com which is pretty nice to see, except for the fact that last I checked something like GOG doesn't run on Linux natively, though thankfully something like Lutris exists.