Hello folks,
I’ve got a beta out for DiscourseHub that should fix this issue. If you’re interested in testing the beta, please use this link: TestFlight - Apple
Note that this is a bigger change in behaviour than just a bug fix, DiscourseHub now follows the same logic as the new user menu introduced in core >9 months ago. The main difference from before is that opening the user menu in the web app will clear the notification counts in DiscourseHub as well (for that site, of course).