As you can Run MusiBee, can you install a typical Win browser like Chrome?
Have you verified the tags are actually populated?
Ok, I finally figured this out, although I'm still a bit confused. I installed Chrome (in the Windows 11 installation in Parallels), but the problem persisted. Then I realized that the description within the Web links configuration menu actually states that the search is for the playing track. Since I don't use MB for playing, no track was "loaded". When playing a track, the links work. After stopping, the album seems "loaded" in the Track Information panel, and will be the one I search for when clicking the links, even if I stop the playback. Then I have to press play on a track in a different album to "activate" this album and make the links work.
I have no recollection of this behaviour previously, is this new? I must admit, I don't really see the rationale?