I realize it's meant for 3.0.x, but drumanuel's stop-disabling-checkboxes-3416333-5.patch seems to work great with our site using Facets 2.0.9, resolving the issue in both Chrome and Firefox.
Having the same issue on Drupal 9.5.8 with Facets 2.0.6. Core search enabled, indexed, and correctly outputting to /search/node. Yet Facets config reports no facet sources, and admin/config/search/facets/add-facet results in the same. No errors or warnings in Watchdog.