I assume that you’ve already logged in, and is trying to unlock the vault through Windows hello (using PIN). The differences between the two states, logged out and locked, are described here: Unlock with PIN | Bitwarden Help Center
My experience with Firefox and BW extension is, clicking on the icon on the browser’s extension bar is unreliable when unlocking. Sometimes, you’ll have to do it multiple times to unlock. Since I am using fingerprint, this is often OK.
The more reliable workaround is to use the sidebar, activated by ctrl-alt-y, and unlock from there. I don’t remember its ever asking to authenticate repeatedly (unlike the browser’s bar icon). The only failure that sometimes pops up is the extension can’t communicate with the desktop app, which can be fixed by bringing the app to the foreground (even without unlocking), and closing the sidebar and then reopening again.
Good luck.