Edit: Solved!

~~Edit2: Partially solved. Issue resolved on this instance, but the other instance doesn't have a "mark as read" button.~~

Edit3: Fully solved. There needs to be a visible message for the "mark all as read" button to appear, which did remove the phantom messages on that instance. Turns out I had "hide bot posts" enabled on both instances, and all the hidden/ghost messages were from bots.

I have a "1 message unread" icon that permanently displays. When I attempt to check my message, the unread messages field appears blank, as if I have read all my messages, but at the top of the page the bell icon still shows 1 unread. New messages increment from one, rather than zero, too. On another instance I just got to 2 permanent phantom unread messages. How do I make this go away?

Also, turmoil has engulfed the Galactic Republic. The taxation of trade routes to outlying star systems is in dispute. Hoping to resolve the matter with a blockade of deadly battleships, the greedy Trade Federation has stopped all shipping to the small planet of Naboo. While the congress of the Republic endlessly debates this alarming chain of events, the Supreme Chancellor has secretly dispatched two Jedi Knights, the guardians of peace and justice in the galaxy, to settle the conflict...

Pic unrelated.