Service Worker (`sw.js`) is not working correctly for Firefox Browser -> Cannot view authenticated Media anymore

### Steps to reproduce

1. Use Firefox Browser (or Firefox based like Tor)
2. Use any up-to-date Element instance. e.g. https://app.element.io
3. Log into a Homeserver with [authenticated media](https://element-hq.github.io/synapse/latest/usage/configuration/config_documentation.html?highlight=enable_authenticated_media#enable_authenticated_media) enabled.
4. Now Pictures wont load with a very high chance and Videos basically never work.

### Outcome

#### What did you expect?
To view the Media, e.g. the picture or video

#### What happened instead?

A 404 request got returned because the old `/_matrix/media/v3/download` URL got called by element web, instead of the new `/_matrix/client/v1/media/download` URL


```
# Element web request

2024-11-02 10:30:08,471 - synapse.access.http.8008 - 428 - DEBUG - GET-4928 - 192.168.178.1 - 8008 - Received request: GET /_matrix/media/v3/download/jameskitt616.one/wfDMUEttAKzpoDtwESGuIMgy?allow_redirect=true
2024-11-02 10:30:08,473 - synapse.http.server - 130 - INFO - GET-4928 - SynapseError: 404 - Not found
2024-11-02 10:30:08,473 - synapse.access.http.8008 - 473 - INFO - GET-4928 - 192.168.178.1 - 8008 - {None} Processed request: 0.002sec/0.000sec (0.001sec, 0.000sec) (0.000sec/0.001sec/1) 45B 404 "GET /_matrix/media/v3/download/jameskitt616.one/wfDMUEttAKzpoDtwESGuIMgy?allow_redirect=true HTTP/1.1" "Mozilla/5.0 (X11; Linux x86_64; rv:132.0) Gecko/20100101 Firefox/132.0" [0 dbevts]

# Cinny web request

2024-11-02 10:30:16,844 - synapse.access.http.8008 - 428 - DEBUG - OPTIONS-5043 - 192.168.178.1 - 8008 - Received request: OPTIONS /_matrix/client/v1/media/download/jameskitt616.one/wfDMUEttAKzpoDtwESGuIMgy?allow_redirect=true
2024-11-02 10:30:16,844 - synapse.access.http.8008 - 473 - DEBUG - OPTIONS-5043 - 192.168.178.1 - 8008 - {None} Processed request: 0.000sec/-0.000sec (0.000sec, 0.000sec) (0.000sec/0.000sec/0) 0B 204 "OPTIONS /_matrix/client/v1/media/download/jameskitt616.one/wfDMUEttAKzpoDtwESGuIMgy?allow_redirect=true HTTP/1.1" "Mozilla/5.0 (X11; Linux x86_64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/130.0.0.0 Safari/537.36" [0 dbevts]
```

### Operating system

Linux Fedora 41

### Browser information

Firefox 132.0

### URL for webapp

https://app.element.io/, https://element.jameskitt616.one/

### Application version

jameskitt616 version: 1.11.83 Crypto version: Rust SDK 0.7.2 (7a21514), Vodozemac 0.7.0;;;;;;;Element version: 1.11.83 Crypto version: Rust SDK 0.7.2 (7a21514), Vodozemac 0.7.0

### Homeserver

matrix.jameskitt616.one Synapse 1.118.0

### Will you send logs?

No

Start with sw.js and reproduce the authenticated-media request in Firefox using the Element web instance described. Compare the old /_matrix/media/v3/download path with the /_matrix/client/v1/media/download path shown in the report. Done means authenticated pictures and videos load in Firefox without the 404 request.

Written by the indexing model from the issue text.