Bump the client-side timeout for /state (#14912)

* Bump the client-side timeout for /state

to allow faster joins resyncs the chance to complete for large rooms.
We have seen this fair poorly (~90s for Matrix HQ's /state) in testing,
causing the resync to advance to another HS who hasn't seen our join yet.

* Changelog

* Milliseconds!!!!

changelog.d/14912.misc

@@ -0,0 +1 @@
+Faster joins: allow the resync process more time to fetch `/state` ids.

synapse/federation/transport/client.py

@@ -102,6 +102,10 @@ class TransportLayerClient:
             destination,
             path=path,
             args={"event_id": event_id},
+            # This can take a looooooong time for large rooms. Give this a generous
+            # timeout of 10 minutes to avoid the partial state resync timing out early
+            # and trying a bunch of servers who haven't seen our join yet.
+            timeout=600_000,
             parser=_StateParser(room_version),
         )