Duplicate notifications on some homeservers (EW and ED)

### Steps to reproduce

1. Receive a 'notification-worthy event'- eg quote reply, @-mention
2. Observe notification

### Outcome

#### What did you expect?

One notification per event

#### What happened instead?

Two notifications

#### More Info

For some time since before Jan 2023 I have been getting two notifications for EW when using Firefox (though I have no discovered this repros with ungoogled-chromium and ED).

For example:

_(contemporanous screenshot I took)_

Differing versions of EW repro:

Thanks to the efforts of @awtj8o81ryywg793 from the EWED chat room I was able to test this further. It also happens:

- with older Firefox versions (back to early 2023)
- with fresh install of Firefox via Flatpak
- with Debian liveCD Firefox (ie no profile)
- with my own slightly older EW instance (1.11.110)
- with app.element.io
- across DMs and rooms

It does not seem to happen on m.org instance, but another user on a different homeserver also reported double notifications at the time- I've asked them if they still do.

I _think_ sounds are also getting duplicated but this is harder to quantify- if there's a good way to establish this I would welcome input on how to go about doing so. The only potential confirmation I can see is the following in the console after receving a double notification:

```js
Got sound default for !gCrAGXFjApFiLyrWQx:matrix.bertieb.org (2)
```

While testing, I discovered this also repros on ungoogled-chromium 139.0.7258.66

ungoogled-chromium:

m.org ungoogled chromium:

And it also repros on Element Desktop:

Since this may be idiosyncratic to particular a HS / HSen, there might be an issue with synapse; I am happy to re-report the issue over there. But for now I am raising this here as there is _probably_ a case to be made that EW/ED should not double notify even if there's some inconsistency with what it receives from the HS :)

I am happy to supply more info of course.

### Operating system

Arch Linux

### Browser information

Firefox 144.0.2

### URL for webapp

develop.element.io

### Application version

b50fbe2eea95-js-df88edfda0aa

### Homeserver

synapse 1.137.0

### Will you send logs?

Yes