Equiping the belt after switching into the form without it won’t start the rage regeneration either, so it seems to be saved when switching forms and doesn’t get updated afterwards
This isn’t a bug, it’s how stats are snapshot for forms, minions & “duration” skills, but it’s probably not desirable in all cases. The Kermode’s chest (white fur for the Werebear) is the same & that’s been the case for years.