Complement `Device_list_tracking_for_pre-existing_members_in_partial_state_room` flake

This issue has been migrated from [#16310](https://github.com/matrix-org/synapse/issues/16310).

---

https://github.com/matrix-org/synapse/actions/runs/6169075347/job/16742675906#step:5:26424

```
client.go:787: [CSAPI] POST hs1/_matrix/client/v3/register => 200 OK (75.192772ms)
client.go:787: [CSAPI] GET hs1/_matrix/client/v3/capabilities => 200 OK (20.201327ms)
server.go:170: Creating room !0-1kyqpkiaQWlFrJMJKD:host.docker.internal:41369 with version 10
federation_room_join_partial_state_test.go:4400: Registered state_ids handler for event $ZTc4bUqYvLVu6w95OtxitUFRQhHntJ7lWu9IeQYpwDE
federation_room_join_partial_state_test.go:4441: Registered /state handler for event $ZTc4bUqYvLVu6w95OtxitUFRQhHntJ7lWu9IeQYpwDE
2023/09/13 07:28:13 Received send-join of event $8mHTdVcQHH4zxXQPeYkdzdQmq4LppMXziDzURot235g
federation_room_join_partial_state_test.go:4379: Incoming state_ids request for event [$ZTc4bUqYvLVu6w95OtxitUFRQhHntJ7lWu9IeQYpwDE] in room !0-1kyqpkiaQWlFrJMJKD:host.docker.internal:41369
client.go:787: [CSAPI] POST hs1/_matrix/client/v3/join/!0-1kyqpkiaQWlFrJMJKD:host.docker.internal:41369 => 200 OK (656.497916ms)
federation_room_join_partial_state_test.go:4294: /join request completed
federation_room_join_partial_state_test.go:2646: Incoming POST /_matrix/federation/v1/user/keys/query
client.go:787: [CSAPI] POST hs1/_matrix/client/v3/keys/query => 200 OK (60.372479ms)
federation_room_join_partial_state_test.go:2646: Incoming POST /_matrix/federation/v1/user/keys/query
client.go:787: [CSAPI] POST hs1/_matrix/client/v3/keys/query => 200 OK (14.998594ms)
federation_room_join_partial_state_test.go:2646: Incoming POST /_matrix/federation/v1/user/keys/query
client.go:787: [CSAPI] POST hs1/_matrix/client/v3/keys/query => 200 OK (8.988556ms)
federation_room_join_partial_state_test.go:2646: Incoming POST /_matrix/federation/v1/user/keys/query
client.go:787: [CSAPI] POST hs1/_matrix/client/v3/keys/query => 200 OK (8.174451ms)
client.go:787: [CSAPI] GET hs1/_matrix/client/v3/sync => 200 OK (212.12803ms)
client.go:787: [CSAPI] GET hs1/_matrix/client/v3/sync => 200 OK (54.750743ms)
federation_room_join_partial_state_test.go:2864: Alice successfully received event $CIrUCeIk4u1DfxqrHRujPoYiLwsdEnlsHc4F6nhC89A via /sync
client.go:787: [CSAPI] GET hs1/_matrix/client/v3/sync => 200 OK (126.832296ms)
federation_room_join_partial_state_test.go:2874: Alice successfully received event $0b2VJAFH-GHDBpUZtvpkRZfXGKAWLRFRegrsYscrUGw via /sync
federation_room_join_partial_state_test.go:4386: Replying to /state_ids request for event [$ZTc4bUqYvLVu6w95OtxitUFRQhHntJ7lWu9IeQYpwDE]
federation_room_join_partial_state_test.go:4419: Incoming state request for event [$ZTc4bUqYvLVu6w95OtxitUFRQhHntJ7lWu9IeQYpwDE] in room !0-1kyqpkiaQWlFrJMJKD:host.docker.internal:41369
federation_room_join_partial_state_test.go:4427: Replying to /state request for event [$ZTc4bUqYvLVu6w95OtxitUFRQhHntJ7lWu9IeQYpwDE]
client.go:787: [CSAPI] GET hs1/_matrix/client/v3/rooms/!0-1kyqpkiaQWlFrJMJKD:host.docker.internal:41369/members => 200 OK (541.301394ms)
federation_room_join_partial_state_test.go:2878: @t30alice:hs1's partial state join to !0-1kyqpkiaQWlFrJMJKD:host.docker.internal:41369 completed.
client.go:787: [CSAPI] GET hs1/_matrix/client/v3/sync => 200 OK (85.939939ms)
client.go:787: [CSAPI] GET hs1/_matrix/client/v3/keys/changes => 200 OK (37.703037ms)
federation_room_join_partial_state_test.go:2618: Incoming GET /_matrix/federation/v1/user/devices/@charlie:host.docker.internal:41369
client.go:787: [CSAPI] POST hs1/_matrix/client/v3/keys/query => 200 OK (44.473879ms)
federation_room_join_partial_state_test.go:2618: Incoming GET /_matrix/federation/v1/user/devices/@derek:host.docker.internal:41369
client.go:787: [CSAPI] POST hs1/_matrix/client/v3/keys/query => 200 OK (65.095108ms)
client.go:787: [CSAPI] POST hs1/_matrix/client/v3/keys/query => 200 OK (56.765456ms)
client.go:787: [CSAPI] POST hs1/_matrix/client/v3/keys/query => 200 OK (21.296433ms)
federation_room_join_partial_state_test.go:4317: Cleaning up after test...
client.go:787: [CSAPI] GET hs1/_matrix/client/v3/rooms/!0-1kyqpkiaQWlFrJMJKD:host.docker.internal:41369/members => 200 OK (19.942625ms)
federation_room_join_partial_state_test.go:4319: @t30alice:hs1's partial state join to !0-1kyqpkiaQWlFrJMJKD:host.docker.internal:41369 completed.
client.go:787: [CSAPI] POST hs1/_matrix/client/v3/rooms/!0-1kyqpkiaQWlFrJMJKD:host.docker.internal:41369/leave => 200 OK (281.747766ms)
federation_room_join_partial_state_test.go:157: host.docker.internal:41369 timed out waiting for @t30alice:hs1 to leave test room !0-1kyqpkiaQWlFrJMJKD:host.docker.internal:41369.
```

In particular

> federation_room_join_partial_state_test.go:157: host.docker.internal:41369 timed out waiting for @t30alice:hs1 to leave test room !0-1kyqpkiaQWlFrJMJKD:host.docker.internal:41369.

Start with federation_room_join_partial_state_test.go, especially cleanup around line 157 and the test named in the title. Reproduce the flake from the linked GitHub Actions log and trace why the leave wait times out. Done means the test reliably completes cleanup without the timeout.

Written by the indexing model from the issue text.