I installed the game on linux using proton (from Properties, Compatibility I ticked to force a Steam Play compatibility tool, I chose Proton Experimental).

I tried to run it, but it returned me the followin error message:

Patrician 3: Please run "P2Setup.exe" to test your video card prior to starting the game.

I fixed the issue as follows. I opened a terminal and prompted the following commands:

cd ~/.steam/steam/steamapps/compatdata/33570/pfx/ env WINEPREFIX=$PWD winecfg

Then I set Windows 7 in the Applications tab. I downloaded the reg file "Patrician_3_Win7_64bit.reg" from the website https://support.gog.com (I found it here: https://support.gog.com/hc/en-us/articles/212451369-Patrician-3-The-resolution-800x600x16-could-not-be-initialised?product=gog but this link might expire) I moved the reg file on the folder ~/.steam/steam/steamapps/compatdata/33570/pfx/ then, in a terminal in that folder I run

env WINEPREFIX=$PWD wine start regedit.exe Patrician_3_Win7_64bit.reg

Apart from this initial bug, the game was just fine.