Timeout joining big remote rooms

This issue has been migrated from [#16683](https://github.com/matrix-org/synapse/issues/16683).

---

Sorry for filing a support request but I can't join `#synapse:matrix.org` because of this problem.

Tried looking at other issues. Some are old with fixes (which obviously does not apply here since the fixes are included) and others don't really have an answer or are closed without resolve.

When joining (preview works) for example `#synapse:matrix.org` after a while this appears in the logs,
```

2023-11-24 12:08:48,322 - synapse.replication.http.membership - 89 - INFO - POST-19608 - remote_join: @zib:xmr.se into room: !ehXvUhWNASUkSLvAGP:matrix.org
2023-11-24 12:08:48,767 - synapse.http.matrixfederationclient - 348 - INFO - POST-19608 - {GET-O-1935} [matrix.org] Completed request: 200 OK in 0.45 secs, got 514 bytes - GET matrix-federation://matrix.org/_matrix/federation/v1/make_join/%21ehXvUhWNASUkSLvAGP%3Amatrix.org/%40zib%3Axmr.se?ver=1&ver=2&ver=3&ver=4&ver=5&ver=6&ver=7&ver=8&ver=9&ver=10&ver=11
2023-11-24 12:09:26,428 - synapse.http.matrixfederationclient - 348 - INFO - POST-19608 - {PUT-O-1937} [matrix.org] Completed request: 200 OK in 37.66 secs, got 49098167 bytes - PUT matrix-federation://matrix.org/_matrix/federation/v2/send_join/%21ehXvUhWNASUkSLvAGP%3Amatrix.org/%24RTRSjwHh4xBZVO5gche9Ri3sj_yLKESeifa1C4CYrEs?omit_members=false
2023-11-24 12:13:52,344 - synapse.http.client - 932 - INFO - POST-9058 - Error sending request to POST synapse-replication://master/_synapse/replication/remote_join/%21ehXvUhWNASUkSLvAGP%3Amatrix.org/%40zib%3Axmr.se/XGkCQlkQMB: RequestTimedOutError 504: Timeout waiting for response from remote server
2023-11-24 12:14:07,398 - synapse.http.server - 124 - INFO - POST-21356 - SynapseError: 500 - Internal server error
2023-11-24 12:14:07,398 - synapse.http.server - 776 - WARNING - POST-21356 - Not sending response to request , already disconnected.
2023-11-24 12:14:07,411 - synapse.http.client - 923 - INFO - POST-9058 - Received response to POST synapse-replication://master/_synapse/replication/remote_join/%21ehXvUhWNASUkSLvAGP%3Amatrix.org/%40zib%3Axmr.se/XGkCQlkQMB: 500
2023-11-24 12:14:07,423 - synapse.access.http.8086 - 465 - INFO - POST-9058 - ... - 8086 - {@zib:xmr.se} Processed request: 319.213sec/0.000sec (0.007sec, 0.000sec) (0.003sec/0.050sec/10) 55B 500 "POST /_matrix/client/v3/join/%23synapse%3Amatrix.org?server_name=matrix.org HTTP/1.0" "Mozilla/5.0 (Windows NT 10.0; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Element/1.11.50 Chrome/118.0.5993.89 Electron/27.0.2 Safari/537.36" [0 dbevts]

Client error : MatrixError: [500] Internal server error (https://xmr.se/_matrix/client/v3/join/%23synapse%3Amatrix.org?server_name=matrix.org)
```

Increasing client_timeout under federation does not seem to help.

Thank you