Fix https://github.com/matrix-org/synapse/issues/14390

 - Client API: `/_matrix/client/unstable/org.matrix.msc3030/rooms/<roomID>/timestamp_to_event?ts=<timestamp>&dir=<direction>` -> `/_matrix/client/v1/rooms/<roomID>/timestamp_to_event?ts=<timestamp>&dir=<direction>`
 - Federation API: `/_matrix/federation/unstable/org.matrix.msc3030/timestamp_to_event/<roomID>?ts=<timestamp>&dir=<direction>` -> `/_matrix/federation/v1/timestamp_to_event/<roomID>?ts=<timestamp>&dir=<direction>`

Complement test changes: https://github.com/matrix-org/complement/pull/559

* Expose getting SYNAPSE_WORKER_TYPES from external, allowing override of workers requested.

* Add WORKER_TYPES variable option to complement.sh script that passes requested workers into start_for_complement.sh entrypoint.

* Update docs to reflect this new ability.

* Changelog

* Don't rely on soft wrapping to format long strings

Good idea dklimpel. Thanks for catching that.

Co-authored-by: Dirk Klimpel <5740567+dklimpel@users.noreply.github.com>

* Small nits just noticed in docs.

* Fixup new line in docs.

Co-authored-by: Dirk Klimpel <5740567+dklimpel@users.noreply.github.com>

Co-authored-by: Eric Eastwood <erice@element.io>

When building the docker images for complement testing, copy a preinstalled
complement over from a base image, rather than apt installing it. This avoids
network traffic and is much faster.

Improve startup times in Complement test runs against workers, particularly in CPU-constrained environments. (#13127)

Co-authored-by: Richard van der Hoff <1389908+richvdh@users.noreply.github.com>

If no database is configured explicitly, use sqlite.

This means that you don't have to pass any variables into the image.

Co-authored-by: Richard van der Hoff <1389908+richvdh@users.noreply.github.com>

When we join a room via the faster-joins mechanism, we end up with "partial
state" at some points on the event DAG. Many parts of the codebase need to
wait for the full state to load. So, we implement a mechanism to keep track of
which events have partial state, and wait for them to be fully-populated.

Fixes matrix-org/complement#330 (or it will, once we remove the old files).

It's not quite a lift-and-shift: I've also taken the opportunity to get rid of the custom CA that we used to use to sign the TLS certs, which has been superceded by the CA exposed by Complement.