(Honestly, the web app is a little janky. Not sure about other apps.)
The trick I used to get it to stop indicating a message for anyone who might want to know:
On the "inbox page" (/inbox in your instance), switch from "Unread" to "All".
(Get ready because there's a timing component to the next three steps.)
Switch back from "All" to "Unread."
The "Mark All As Read" button should appear at least momentarily while the page is loading.
As soon as you can, start rapidly spamming the "Mark All As Read" button and cross your fingers.
If you're lucky, that did the trick and it won't display a "1" on your bell icon. If not, repeat from step one. It shouldn't take much more than three or four tries to make it work.