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?
When you say it seems to have better HDR, is that deduced from watching the video or looking at these screen shots? Because if we're talking about the screen shots I'd have to disagree.