Integration tests

~~Currently there are no integration tests for the project which makes changing anything risky.~~

Ok so I have updated this with what has been done and what there is yet to do:

- [x] integration tests can now be added to test/integration which are run using `yarn test:integration` with mocha
- [x] A test environment that sets up synapse that "just works" with the tests can be started using [mx-tester](https://crates.io/crates/mx-tester) which has its own config in `mx-tester.yml`
- [x] The integration tests are run as part of the github CI
- [ ] There are tests for more things

Start in test/integration and read mx-tester.yml; run yarn test:integration to see the existing Mocha integration coverage. Review the remaining project areas that need tests and define a specific coverage target before adding them. Done means the selected integration tests pass locally and in GitHub CI.

Written by the indexing model from the issue text.