• White Screen after the logo, menu accessible using tab but not usable
  
• Connection Error 395 after putting in your birth month
  
• Black Screen on start

Enable Compatibility for all Steam Games (if you haven't already)

To play Umamusume: Pretty derby you have to enable "Steam Play for all Titles" since it doesn't have native Linux support.
Its in the steam settings which you can access by

• Click Steam in the top right
  
• Click Settings near the bottom of the popup
  
• In the Settings, go to Compability under "In Game" and over "Controller"
  
• Enable Steam Play for all Titles

Install ProtonUp-Qt and add GE-Proton

To install ProtonUp-Qt in most distros, simply use this Command

• flatpak install flathub net.davidotek.pupgui2

After the Installation, launch the ProtonUp-Qt tool using the shortcut in the Menu of your distro and do the following

• Select Steam at the top if not selected already.
  
• Click the "Add Version" button at the bottom left, above the version info
  
• Usually, the most current version of GE-Proton is already selected, if not, select "GE-Proton" and "GE-Proton-10"
  
• My Primary Source used GE-Proton-3 but -10 worked fine for me
  
• Select Install and wait for it to install
  
• You can close the window after the installation is done.

Select GE-Proton as the compatibility for Umamusume: Pretty derby

You can choose if you would rather GE-Proton for just umamusume: pretty derby or for all non-native games.

Just for Umamusume: Pretty derby:

• Go to your Library
  
• Right Click "Umamusume: Derby Pretty"
  
• Select Properties
  
• Go to Compatibility
  
• Check the Box for "Force the Use of a specific Steam Play Compatibility tool"
  
• Select "GE-Proton-10"

For the entire Library (thats not native to linux)

• Click the Top Right Steam
  
• Go to Compatibility
  
• Select GE-Proton-10
  
• Restart Steam if it asks you

If this fixed Umamusume: Bakushin Derby for you please dont tell me.
If this didnt fix Umamusume: Pretty Derby for you please do tell me and click the Thumbs down as Feedback.

Sources:
https://gtm.steamproxy.vip/app/3224770/discussions/0/598532007497043071/#c594028416743784577
-> Found this after the Guide but is good too
-> Also shows usage of GE-Proton and fix
https://gtm.steamproxy.vip/app/3224770/discussions/0/597406800760823404/
-> Steam Discussion about the connection error 395 on Linux Mint
-> Linked to the Link below and showed that GE-Proton is a good Fix for this.
https://github.com/ValveSoftware/Proton/issues/8848
-> Official Proton github, Issue is about Umamusume: Pretty Derby
-> Niruchie explained their Fix near the bottom of the page, the one with the screenshots.