I don’t think it does, but I would pay for this.

Are you able to pull game categories or genres with Heroic or Lutris? For example, to search for local multiplayer games, puzzle games, etc…

How well does https://www.protondb.com/ hold up when checking Proton compatibility with GoG?

Nice! Valve has done a lot for gaming on Linux, its one of the main reasons I use Steam.

What do you recommend on GoG?

I wouldnt pay for anything full price.