+1 on this, exactly the same situation.
The plugin worked correctly before, but I had to reinstall MusicBee on a clean Windows install, and it stopped scrobbling. I have re-checked login details several times, re-installed MusicBee, everything.
Latest MusicBee, Windows 10 20H2.
What I did to fix it, is go to my account settings, find MusicBee in the "Applications" tab, and clicked "Disconnect".
I then re-connected inside MusicBee, and it started to scrobble correctly.