Test global profile compliance

[ShadowJonathan]

This is mainly a response to matrix-org/synapse#5677, I'd wish to test for bugs reported and talked about in that thread, to make sure these don't re-surface in synapse or in other servers, and ensures compliance to the spec in general.

The cases that trigger those bugs seem to be fairly complex and setup-specific, something which complement was built for, thus this issue.

[DMRobertson]

I had something for this in #199, but we dropped them for now. See #199 (comment)
and 56bf3e3