Problem: For example, if you type "Wikidata:Project ch" it should suggest the Wikidata page (not item) for Project chat. Currently the SearchAll gadget is used as a workaround.
Proposed solution: Ideally, get rid of Wikidata overriding the whole search box, and instead make it run standard API request and have small(er) pluggable Wikidata part than runs the second request.