I keep having the same issue of not being able to create a new save file just as commented before. I tried with various versions of proton including the latest one at the time of writing (5.0-4)

Fortunately I was able to make it work following the steps of the first review. (Thanks a bunch maldun.finsterschreck!!!)

I would just like to add couple of tips for the Linux newbies such as me.

If you are having trouble creating the necessary folder with the terminal follow these steps:

1.- Select the game on your steam library click on the "Manage" button (Gear icon) then click on "properties go to the "Local files tab" and finally click on the "browse local files" button.

2.- You will find yourself on the route "steam/debian-installation/steamapps/common/Senran Kagura Burst ReNewal"

This will depend on your file manager but, you can either click on the "steamapps" button on the route or erase everything after "steamapps" and hit enter

3.- Once you are on the steamapps folder just follow the route:

p~/.local/share/Steam/steamapps/compatdata/889510/pfx/drive_c/users/steamuser/AppData

4.- Create a new folder and name it "Local" (in my case I only had one named "LocalLow")

5.- Open the folder you just created and create a new one called "Senran Kagura Burst ReNewal"

6.- Restart the game and you should be good to go ;)