OK, after consulting with Ken-ichi, it’s not a bug but intended behavior.
“The Identifiers tab in Obs Search shows the people who have added identifications to observations in the current search, not people who have added identifications of the taxon filtering the current obs search. I am fairly sure that was intentional, as obs search could have multiple filters applied to it that may or may not have anything to do with taxa”
Well, with the caveats mentioned above, you can use inaturalist.og/explore and search for a taxon, then click on “Identifiers” to see a list of the top identifiers of observations of that taxon.