Update avatar also updates per room display name

This issue has been migrated from [#16059](https://github.com/matrix-org/synapse/issues/16059).

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### Description

Setting a new avatar via /_matrix/client/v3/profile/{userId}/avatar_url also changes the per room display name in all rooms to the display name set in the user's profile.

### Steps to reproduce

- in at least one room set a different display name with `/myroomnick nickname` for example with element or element web
- go the your profile settings
- set only a new avatar
- click save

expected behavior:
The avatar and only the avatar is updated in all rooms

what actually happens:
Room specific display names are also updated to the display name configured in your user profile

### Homeserver

https://matrix.ccc-ffm.de

### Synapse Version

1.88.0

### Installation Method

Debian packages from packages.matrix.org

### Database

PostgreSQL

### Workers

Single process

### Platform

Debian 11, virtual machine

### Configuration

nope

### Relevant log output

```shell
no relevant logs created
```

### Anything else that would be useful to know?

The client only sends a request to update the avatar but the server also updates the display name.

The only request send is the following put request: `/_matrix/client/v3/profile/{userId}/avatar_url` as specified in https://spec.matrix.org/v1.7/client-server-api/#put_matrixclientv3profileuseridavatar_url