The search results that are currently shown in the AutosuggestSitelink gadget are based on a search for the current page's title (without namespace). This works sometimes, but as tasks such as T329967 indicate, there are variations on the page title that would be useful to be able to search for.
To make it most flexible, it could be a good idea to add a search box above the search results, prefilled with the current title but modifiable by the user. The search results would dynamically update with the same behaviour as the autocomplete does for the main search box on Wikidata.
