Authenticated media does not work in Firefox private browsing mode

### Steps to reproduce

1) Open Element Web (e.g. app.element.io) in a Firefox Incognito Window.
2) Join some rooms (if not already in some)
3) Check Developer Console

### Outcome

#### What did you expect?

Element to show all room pictures and user avatars

#### What happened instead?

Some room pictures and user avatars (and possibly other pictures) are not loaded. If I open it in a normal (not incognito) window on the same browser, it works fine.

### Operating system

MacOS

### Browser information

Firefox 133.0 (aarch64) on MacOS 14.5

### URL for webapp

app.element.io

### Application version

Element version: 1.11.87 Crypto version: Rust SDK 0.7.2 (517d99b), Vodozemac 0.7.0

### Homeserver

matrix.org and self hosted

### Will you send logs?

Yes