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?
Once you get a devops pipeline set up, you do all versions at the same time and have the compiler farm handle it. No reason the native versions shouldn't be receiving updates at the same time when its become rather easy to integrate multiple targets at the same time.