"active" notification doesn't seem to go away no matter what I look at

### Steps to reproduce

1. Go to app.gitter.im
2. See the * on the title bar indicating an "active" notification
3. Look at lots of things to try to make it go away
4. Cry

### Outcome

#### What did you expect?

No asterisk after catching up and reading everything.

#### What happened instead?

Tears.

### Operating system

macOS

### Browser information

Chrome

### URL for webapp

app.gitter.im

### Application version

_No response_

### Homeserver

_No response_

### Will you send logs?

Yes

Start by reproducing the persistent asterisk at app.gitter.im in Chrome on macOS, following the listed steps and checking whether reading all notifications changes it. Trace the notification state from the observed behavior, then verify that the title bar has no asterisk after everything is caught up.

Written by the indexing model from the issue text.