Over a hundred `/_matrix/client/v3/rooms/{room}/event/{event}` requests blocking startup.

### Steps to reproduce

1. Load element-web.
2. Close tab.
3. Load element-web.

### Outcome

#### What did you expect?

It loads quickly.

#### What happened instead?

It takes over 20s on a very fast connection and makes hundreds of requests event despite little to no new events occurring and only 27 rooms being visible in the room list.

(Preloading more events may be a good idea, but it shouldn't block the main message list being visible)

### Operating system

Linux

### Browser information

Firefox 140.0.4

### URL for webapp

app.element.io

### Application version

Element version: 1.11.106 Crypto version: Rust SDK 0.12.0 (b30f1f3), Vodozemac 0.9.0

### Homeserver

matrix.org and others

### Will you send logs?

Yes

Reproduce the startup flow in Firefox 140.0.4 on app.element.io by loading Element, closing the tab, and loading it again while observing the /_matrix/client/v3/rooms/{room}/event/{event} requests. Trace which startup work creates the request burst and verify that the main message list becomes visible without waiting over 20 seconds.

Written by the indexing model from the issue text.