It is a workaround to make identification a bit easier rather than a true solution, but I believe it should be possible to add this to the URL to find observations marked as captive/cultivated while excluding observations that are casual for other reasons:
&fails_dqa_wild=true
(From this thread: https://forum.inaturalist.org/t/how-to-use-inaturalists-search-urls-wiki-part-2-of-2/18792/)