Convert synapse-specific sytests to subfolder here

This issue has been migrated from [#14547](https://github.com/matrix-org/synapse/issues/14547).

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Currently, complement has a [list of ignored sytests](https://github.com/matrix-org/complement/blob/main/sytest.ignored.list), which roughly includes three categories;
- Dummy tests
- Tests that test with deprecated endpoints
- Synapse specific behaviour

Under the latter fall endpoint tests such as `/_synapse/admin`, but also [synapse-specific behaviour](https://github.com/matrix-org/complement/pull/554/files#diff-dc319127f18082901e740891fd898079bea72d6a43235dedc736b83e68b07546R19-R32) that can't be put into complement due to it not being able to be backed up by the spec.

While the latter will be resolved in due time, the former (categorically) cannot, and so this issue serves as a suggestion to **create a subfolder in the repo that contains a set of golang test files that import and utilise the complement internal libraries to run those tests**.

https://github.com/matrix-org/complement/issues/226 is related to this effort, where I suggested this be (reliably) possible by freezing the commit sha that this subfolder would pull complement dependencies from, to alleviate concerns on complement's side to require to stick to a public api.

(Occasional manual updates would still have to happen, but these would be isolated and would deal with the breaking-api-changes in its own PR, without grinding the CI to a halt due to it not being able to compile the tests)

This effort would pave the way for the remaining tests from sytest to find a new home, and allow sytest to be deprecated in due time.