Updating avatar also unsets unread notification counts for all rooms

This issue has been migrated from [#16373](https://github.com/matrix-org/synapse/issues/16373).

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### Description

Similarly to https://github.com/matrix-org/synapse/issues/16059 setting a new avatar via `/_matrix/client/v3/profile/{userId}/avatar_url` also marks all notifications as read, as in, marks all rooms that have "unread notifications" as done.

### Steps to reproduce

- have a room with unread messages
- set a new avatar in your settings
- see the notification count disappearing

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None of the platform-specific details below are relevant; this issue is more to discuss if this behavior is really intended.

### Homeserver

/

### Synapse Version

v1.92.3

### Installation Method

Docker (matrixdotorg/synapse)

### Database

PostgreSQL