I've never really thought about whether the game looks the same using its Windows vs Linux renderer. I installed HL2 to check out the anniversary update and decided to try the Windows renderer on Proton. Would you look at this difference... Linux is the top one, Windows is the bottom:
Is this is a thing? Have you tried other games and seen the Windows version looking better?
The Windows version seems to have better HDR and some differences in textures in this shot. Performance-wise it runs great. I think this might be a case of the opposite, Valve not bothering to get all the changes they did with the 20th anniversary update to work on Linux.
Interesting, although in your screen shots the Linux version looks better? Are the screenshots the wrong way round or maybe just not able to represent the other changes you mention in the game?
The lighting looks better in the first shot and the items like the bin look better. But the textures of the posters look less good.
It seems very odd the game would use different textures at the same resolution and settings. Maybe they made some compromises to get the Linux version working as you say?
Also HDR is notoriously messy on Linux - maybe the Proton version of the game is managing to use it better than the native route on your system? Or maybe they didn't do a good HDR implementation on the Linux version as you say.
Would be interesting if people notice the same of the issue is the Proton version is better than the Linux native version.