UI hangs several seconds, regulary

### Steps to reproduce

Randomly, when trying to use Element-Web, I find that the UI stops responding for a few seconds at a time. When such is the case, character input isn't shown (but buffered, and after a few seconds, it'll appear in the input box). Also, interaction with other UI elements, such as context menus on individual posts, or the room list, isn't possible (no hover effects, and clicks don't have an immediate effect).

### Outcome

It's quite hard to reproduce this in a meaningful way for this bug report, but I managed to capture a profile for the [Firefox Profiler](https://profiler.firefox.com), and there you can see screenshots, as well as UI and network activity. I've put the profile up for download [here](https://scratch.madduck.net/__tmp__madduck__Firefox%202022-12-22%2011.10%20profile.json.gz)

Check out this screenshot for now:


You can clearly see that everything seems to be blocking on a number of network requests, and in fact, it is during these two seconds that the UI wasn't responsive. So while the UI should never block on network, it does appear as if it does in this case.

### Operating system

Debian Linux (unstable)

### Browser information

Firefox 108

### URL for webapp

`develop.element.io` and `app.element.io`

### Application version

Both `app` and `develop` are affected:
* Element version: 85e2f063ac81-react-b81582d04569-js-aead401005fa
* Element version: 1.11.17

### Homeserver

matrix.madduck.net, Synapse 1.74.0

### Will you send logs?

No