Messages taking 15-30 seconds to send in certain rooms

### Steps to reproduce

1. Try to send a message to certain rooms (some friends and I have one group chat where this happens)

### Outcome

#### What did you expect?

The message would take around a quarter of a second to a second at most to send.

#### What happened instead?

It consistently takes around 15-30 seconds for any messages sent from our phones to send to other people in the rooms. We are on multiple homeservers and it is occuring for all of us.

### Your phone model

Google Pixel 6

### Operating system version

Android 13

### Application version and app store

Element 1.6.5 [40106052] (G-fd6a45a3) from Google Play Store

### Homeserver

lilysthings.org synapse 1.91.1

### Will you send logs?

Yes

### Are you willing to provide a PR?

No