Faster room joins: `device_lists.left` not emitted in `/sync` response when completing the join and discovering that a user is actually not in the room

This issue has been migrated from [#13886](https://github.com/matrix-org/synapse/issues/13886).

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See the commented out check in the `TestPartialStateJoin/Device_list_tracking/Device_list_no_longer_tracked_for_user_incorrectly_believed_to_be_in_room` complement test.

That test case is roughly:
1. A room starts with `@charlie:remote`, `@derek:remote` (moderator) and `@fred:remote` (admin)
2. `@fred:remote` leaves the room.
3. `@alice:local` partial state joins the room.
4. `@elsie:remote` joins the room.
5. `@fred:remote` "bans" `@derek:remote`, citing their join event as auth. The local homeserver does not know that `@fred:remote` is no longer in the room and accepts the event.
6. `@derek:remote` kicks `@elsie:remote`. The local homeserver incorrectly rejects the kick because it thinks `@derek:remote` has been banned.
7. The partial state join completes and `@elsie:remote` is discovered to really have been kicked.
8. No `device_lists.left` entry is emitted.

Start with the commented-out check in the TestPartialStateJoin/Device_list_tracking/Device_list_no_longer_tracked_for_user_incorrectly_believed_to_be_in_room complement test. Trace partial-state join completion and the /sync device-list handling, then run this test and verify that completing the join emits the expected device_lists.left entry for the user discovered to have left.

Written by the indexing model from the issue text.