Rework integration tests of REST API server

This reworks some of the tests and modules to decouple the modules some more. Unfortunately, the speedup is not great, but it can avoid some re-running depending on where changes are made. Not all the changes seem necessary, but helped me to understand some underlying issues.

I rewrote one of the tests to use the in-memory implementation, which speeds things up significantly. Keeping it as a system test, I was not able to get the application context running fully. There seems to be little risk associated with the change, and I think we should keep it as is. (I put the file in "unit" tests, because a new test suite for a single file seemed overkill.)

Splitting/Moving the test helper file also helped a bit, but those seem redundant, and we should refactor that at some point; but I did not want to blow up the MR even more.

The most speedups will be had if we can move some of the "system/acceptance" tests out, which I am trying right now.