Try this:
- disable biometrics in the FF extension
- uninstall the Bitwarden desktop app
- install the desktop app again from this download: https://vault.bitwarden.com/download/?app=desktop&platform=windows (don’t use Windows Store version)
- enable biometrics in the desktop app
- enable desktop integration in the app
- enable biometrics in the FF extension
And if necessary, also try this step posted as a solution by @ConsistentCorgi below:
- enable Require verification for browser integration
Hope that works!
EDIT: added one more step by @ConsistentCorgi