But you are asking about Proton which according to wikipedia is a fork of Wine designed for integration into the Steam client as “Steam Play”?
I only play occasionally on Steam so I’m not that kind of a hardcore gamer but as far as I know as a general rule of thumb you play Steam games with Steam and non-Steam games with Lutris, (though you can add games to the Steam client too, but I never tried it), so you’d be better served asking those specific questions in the Lutris forums or in Steam’s Steam Play forums
That’s not new, specific games play with specific settings and Proton/Wine versions so you should always consult wikis and answers in those places and https://www.protondb.com
A lot of people add their non-Steam games to Steam because they want to take advantage of Proton, instead of having to configure WINE + DXVK themselves in Lutris.
And who do you ask if you have Proton problems with non-Steam games, I 've heard Lutris comes with pre-defined settings for games making life even simpler, Overwatch to name an example from the back of my mind. Don’t know the real benefits of Proton, and going a little off-topic of course now, what are they that Lutris can’t handle, when it’s said it does all the configuration for you out of the box?
Non-Steam games can include games from GOG, that are also available on Steam, but the user prefers to buy it from GOG, or another vendor, to avoid DRM or whatever reason.
Direct fixes and patches for games by Valve and the community, such as Cyberpunk 2077 working with Proton but not regular WINE. And I get higher FPS in some games using Proton due to their patches.
And for some games, even better if I use GloriousEggroll’s Proton Fork, such as with anything that uses Media Foundation for cutscenes and videos.
You can see some fixes for official Proton from Valve here. Also, dxvk and vkd3d-proton are integrated in Proton