Multi-second delays in receiving messages

### Steps to reproduce

1. Open Element Web and another client simultaneously
2. Wait for somebody to message you

### Outcome

#### What did you expect?

Element Web receives the message roughly at the same time as the other client.

#### What happened instead?

I first receive a notification on the other client (in my case FluffyChat on Android, also tested with Nheko on macOS). Only after several seconds, I receive the message on Element Web.

### Operating system

macOS 15.7.1

### Browser information

Chrome 142.0.7444.176

### URL for webapp

app.element.io

### Application version

Element version: 1.12.4 Crypto version: Rust SDK 0.14.0 (c3b7918), Vodozemac 0.9.0

### Homeserver

matrix.evolved.systems running Synapse 1.142.1

### Will you send logs?

Yes