Notification panel is empty and stays empty even after new notifications come in

### Steps to reproduce

*As originally reported by @Elliria in https://github.com/vector-im/element-web/issues/24532#issuecomment-1434069184,*

1. Start with a fresh account and a blank notification panel (empty state, "You're all caught up").
- Or alternatively, page-load the app with the notification panel open. This is a [separate Element bug](https://github.com/vector-im/element-web/issues/24663) but is an easy way to get into this state
1. Get some mentions in a public room (not encrypted)
1. Notice that the notification panel doesn't include those mentions that are plainly visible in the app

Mentions not included in notifications panel (screenshot from the @EricGitterTester perspective):


And after a refresh (and switching between rooms), the mentions appeared and new mentions that happen also appear in the list.


While I understand this panel is populated with whatever `/notifications` returns, this feels like it may be an Element problem where it doesn't properly gather notifications once it's shown the empty state.

### Outcome

#### What did you expect?

Mentions are included in notifications panel

#### What happened instead?

All mentions missing

### Operating system

Windows 10

### Browser information

Chrome Version 110.0.5481.100

### URL for webapp

https://app.gitter.im/

### Application version

Gitter version: 1.11.23 Olm version: 3.2.12

### Homeserver

gitter.im

### Will you send logs?

No