iiuc, this bug is only for Bundled Flow Topics. E.g. "2 new topics on Talk:Beta Features/Hovercards"

For the other Flow Messages (for single items), in order to mark each Notification as read, you do need to either:

• Visit the topic (not the board)
• Click the "x" at the right of the Notification
• Click "Mark all as read".

(ie. It will intentionally not mark Messages as read, just by opening the flyout.)

This is happening even when I click on an individual message in the flyout. I know that opening the flyout doesn't clear the marker.

Quiddity, I got it for:

Moderated Topics - update
Quiddity (WMF) created a new topic on Talk:Flow.
33 minutes ago

So it might only be for Flow notifications, it's not only for bundled Flow notifications.

The red box color and number are wrong (still says 1), but it does correctly say:

Alerts (0) Messages (0)

First, the text in the red/non-red box should always be the sum of those two values (Alerts/Messages), AFAICT. So that could be considered a sub-bug.

Second, in this case the link goes to:

https://www.mediawiki.org/w/index.php?title=Talk:Flow&topiclist_sortby=newest&fromnotif=1

I would naturally expect when I click this, it would consider it read, and update the red box.

However, that is a link to the board, so perhaps that is the mismatch (given you said, "Visit the topic (not the board)") above.