Got updated til v38, but my MacMonterey is not supported

Here is how to uninstall

Uninstalling Logos for Mac

Before Uninstalling, recommend restarting Mac (see if issue goes away) and launch to blank layout, see sign-in tip
Note: If using a supported Stable release, before uninstalling, please contact Tech Support if the program does not seem to be functioning properly. An uninstall/reinstall may not be the solution. Beta issue(s) are discussed in Logos Desktop Beta forum
In Finder window, Home icon  appears next to your username for quick access to /Users/usernameFor ~/Library see User Library is Hidden below.

• To Delete an item: can drag item to trash OR right click on item, then click “Move to Trash” OR highlight item, then press Command-Delete.
  Optional: Restart Mac + empty trash after deletion.

1. Before Uninstalling, close (or force quit) Logos and Indexer (if blue Logos icon on menu bar, click icon, then click Cancel).
2. To Uninstall Logos, delete application, caches, launch agent, parameter list (plist), and mono configuration files (username is your login name):
   1. Delete Logos from your Dock
   2. Delete Logos application (nominally from Applications folder)
   3. Delete com.logos.Logos in /Users/username/Library/Caches
   4. Delete com.logos.LogosIndexer in /Users/username/Library/Caches (folder may not exist)
   5. Delete com.logos.LogosIndexer.plist in /Users/username/Library/LaunchAgents
   6. Delete com.logos.Logos.plist in /Users/username/Library/Preferences
   7. Delete com.logos.LogosCEF.plist in /Users/username/Library/Preferences (file may not exist)
   8. Delete com.logos.LogosInstaller.plist in /Users/username/Library/Preferences (file may not exist)
   9. Delete com.logos.Logos.savedState in /Users/username/Library/Saved Application State (folder may not exist)
   10. Delete  logos in /Users/username/.mono/registry/CurrentUser/software (folder .mono nominally hidden)
       • Finder => Go menu => Go to Folder... => ~/.mono/registry/CurrentUser/software (Go) => Delete logos and logos4
         OR
       1. Open Terminal (inside Utility folder in Applications)
       2. rm -rf ~/.mono/registry/CurrentUser/software/logos*
       3. Quit Terminal
   11. Optional: Delete keypairs in /Users/username/.config/.mono/keypairs (folder .config nominally hidden)
       • Finder => Go menu => Go to Folder... => ~/.config/.mono (Go) => Delete keypairs
         OR
       1. Open Terminal (inside Utility folder in Applications)
       2. rm -rf ~/.config/.mono/keypairs
       3. Quit Terminal
3. If want to Completely Uninstall,
   • With download of all your Logos resources, then delete/Users/username/Library/"Application Support"/Logos4 folder
     OR
   • Avoid download by using Copy Logos Resources to macOS, including Note to delete Logos4 folder after saving Resources folder.

It is from the Wiki

You may need to do more to uninstall 38 than you did.

If that does not update you, then try update channel to stable.