Smooth!
Game work out of the box
Works just as well as the Windows version.
The analog input that moves your cursor around the map is inverted. This is mentioned in the Steam forums by several players of the native Windows version, so it's not a Linux/Proton-specific issue. From what I understand, you have to manually lock the game at 60fps to make the analog stick act properly, but there is no way to do this in the game itself as far as I know.
Any issues you experience running this on Linux are likely issues that have already been brought up for Windows on Steam. Namely, the controller issue, along with the game freezing when opening the Graphics menu for the first time (at least, it only happened once for me so far). Here's to hoping the developers can fix these issues, because Brigandine deserves red carpet treatment. Otherwise the game is perfectly playable.