Upgrading large rooms takes 1000s+, times out resulting in confusing client error

### Description

Upgrading large rooms takes more than 10s, but after 10s synapse emits some kind of timeout error, leaving the client in a mess.

### Steps to reproduce

* upgrade a big room in EW with lots of bans (e.g. #element-web:matrix.org which had 15K people in it)
* "failed to fetch" error turns up after 10s leaving room half-upgraded in some horrible limbo: https://github.com/element-hq/element-meta/issues/2530

### Homeserver

matrix.org

### Synapse Version

Whatever was live 2024-07-29T14:23:58.642Z

### Installation Method

Other (please mention below)

### Database

postgres

### Workers

Multiple workers

### Platform

debian

### Configuration

_No response_

### Relevant log output

```shell
Go look at the logs, if they're still there...
```

### Anything else that would be useful to know?

_No response_