Here is how you make it work:
Step 1:
Enable Steam Play
https://store.steampowered.com/steamplay

Step 2: enable Steam Play for everytitle

Step 3:
Download Sengoku with the steam client


Important step 4:
Rename Sengoku.exe to Sengoku-old.exe
&&
Rename SengokuGame.exe to Sengoku.exe

##note
This guide that's fixing the steam overlay might also do the trick, (see the guides rename step). But experience with the older paradox game launchers makes this less optimal. It might not work for your setup.
https://gtm.steamproxy.vip/sharedfiles/filedetails/?id=268463069


Step 5:
Launch Sengoku using the steamclient

UPDATE://
Proton 4.1 and newer might not need these steps, and the launcher should work without much config \


Source:
https://store.steampowered.com/steamplay
https://www.protondb.com/app/73210

Guide Picture by Richard Pluck:
https://flic.kr/p/7aUuVB

Picture Lisence
Attribution-NonCommercial-NoDerivs 2.0 Generic (CC BY-NC-ND 2.0)
https://creativecommons.org/licenses/by-nc-nd/2.0/

and once again thanks to whoever is running Manjaro Linux and submitted the report @
https://www.protondb.com/app/73210