Migrate tests from `notebook.tests` to `jupyter_server` and pytest-style framework

[RRosio]

trafficstars

• [ ] Determine equivalent test structure using jupyter_server’s pytest plugin
• [ ] Replace custom setup/teardown with pytest fixtures:jp_serverapp, jp_fetch etc
  • Currently we import from notebook.tests.*, notebook.notebookapp.* and notebook.utils
    • ServerTestBase, assert_http_error etc
• [ ] Update CI to no longer install notebook<7
• [ ] Remove any compatibility fallbacks once migration is complete

[danyeaw]

#262 depends on removing support for Notebook v6 since it requires Python < 3.10.

[RRosio]

Maybe we can also do a incremental approach to moving tests over to the pytest-jupyter plugin. We can keep the current test suite running and add in another test directory where we begin porting the tests. I was thinking we can start off with a different CI job for these tests, and the base configuration then begin including the necessary fixtures, and tests as we go. cc @danyeaw

[danyeaw]

I like this incremental approach. Since we are already using pytest, could we keep it all part of the same test suite, just migrate a few tests at a time?