Changing display name trigger a device change

This issue has been migrated from [#9392](https://github.com/matrix-org/synapse/issues/9392).

---

### Description

### Steps to reproduce

- change the display name of the user, using `PUT https://matrix-client.matrix.org/_matrix/client/r0/profile/{userId}/displayname`
- It triggers some "join" membership event for every rooms, which is fine
- But it also triggers a device change of the current user in the next sync response:

```json
"device_lists": {
"changed": [
"@userId:matrix.org"
],
"left": []
},
```

- it has the effect to trigger download of device list, key query and lots of shield trust computation, with no reason.

So this is not good for the overall performance of the system (client and server side)

- other members, who share at least a room with the one who change their display name seem not affected by this extra device list change.

### Version information

- **Homeserver**: matrix.org `{"server_version":"1.27.0rc1 (b=matrix-org-hotfixes,844b3e3f6)","python_version":"3.7.3"}`

Start by tracing the PUT /_matrix/client/r0/profile/{userId}/displayname entry point through the next sync response, focusing on device_lists.changed for the user who changed their name. Reproduce the profile update and verify that it does not cause an unnecessary device-list download or key query, while preserving the expected room membership events.

Written by the indexing model from the issue text.