Looking at SteamDB, it looks like it checks VC2015 is installed. So you'll want to check if your bottle has at least one of: vcrun2015, vcrun2017, vcrun2019 or vcrun2022. It's pretty likely that's a required dependancy.
It also installs "DirectX Jun 2010 Redist" which installs or updates a bunch of libraries, I think most if not all of these can be installed to your bottle too. I don't know which are required but it's a place to start.