If this is worth doing (and it probably is) it should also support Notebook 7, to the best of its abilities. As NB7 doesn't have a launcher, it would need to be ported to a file browser dropdown to stay consistent, UX-wise.
There is some work on-going to update documentation for supporting lab4/nb7 in the same extension, which can likely be used here: basically checking whether ILabShell is available should be enough.
Much as I tried (admittedly, not very hard), I ended up not being able to cleanly do keyword-for-keyword compatibility between jquery- and lumino-based notebooks, so the browser-based acceptance tests would need to updated to use the new client keywords.
From @bollwyvl in https://github.com/jupyterhub/jupyter-server-proxy/pull/419#issuecomment-1677987290