This this has always been a temporary hack in order to make it easier for people to leverage statements for searches.
Now that that has been built into MediaSearch, and that the search widget is going to submit to mediasearch, we will no longer need it.
This essentially means removing the wikibase.mediainfo.search module (and all associated code & messages) and removing wbmi-search-suggestions from the preferences.
- Searches from the skin search widget end up at Special:MediaSearch (see T273879)
- Searches from the skin search widget no longer show "files depicting..." autocomplete suggestions
- 'wbmi-search-suggestions' is removed from the search preferences