The ap_verify dataset framework was originally designed on the principle that ap_verify itself should not depend on any obs packages or on any datasets, and that users should set up only those that they need. Datasets have a dependency on the obs package they need, so that the package is (almost) guaranteed to be available if the dataset is set up. As far as I know, the current CI system assumes this behavior.
However, this causes a problem with ap_verify_testdata, because the package is included in some Stack builds despite being only an optional dependency of ap_verify. This causes frequent downloads of ap_verify_testdata, which would be prevented if ap_verify_testdata had no dependencies and it was ap_verify that guaranteed the obs package. This change would make ap_verify_testdata unusable for general processing, but this is already the case because ap_verify_testdata is not registered with ap_verify as a known dataset (but we would no longer be able to remove this special-casing in the future).
ap_pipe_testdata also has a dependency (on obs_decam), but is a conventional test data repository rather than an ap_verify dataset. Its dependencies should also be reworked as part of this ticket.
I think we can keep ap_pipe and ap_verify from having hard dependencies on obs packages if we make them optional. However, this requires reworking the test code that checks if testdata are available; see jointcal for one way to do this.
Removing the obs_lsst dependency will also break ap_verify_testdata's Gen 3 maintenance script. However, as long as it's obvious to the script caller that the problem is a missing package, I don't think anything needs to be done.