Create a special page that allows to enter a query (i.e. enter one property and enter one value, it's type depending on the selected property), run the query, and display the results on the special page.
The special page should not be implemented via an AJAX call, but rather as an HTML result page, using the usual MediaWiki Special page paging mechanism.
In particular, it should allow for an URL like
but if this shows troublesome for some datatypes (e.g. coordinates, time) then instead of blocking on this, implement the other datatypes first.