@Ramsey-WMF that's great! My programming skills are minimal, but I'd be happy to help in other ways.

Just want to add my support for this, especially in terms of structured data for commons images. The structured data is nonexistent in other languages when searching for images in google. I love the move to structured data and its multilingual ability, but if no one can find anything in languages other than English, it's not very useful. Here's an example:

Could we come at it from the other direction? Use the wikidata drop-down result to generate a text search in addition to the haswbstatement results. Set up search so that all words in the search are selected from the drop-down, but then use wikidata's "label" "description" and/or "Also known as" to generate additional results based on those words for a "regular" text search.

I was playing around with the search some more and I think this is actually a lot closer to solved than it appears. In the main search box at the top of the page, when typing in a search term you can select a "depicts" item which then becomes a haswbstatement:P180 item for the search. The problem is there's no easy was to add a second haswbstatement:P180 term. If the advanced (AKA search results) page had the same box or function, maybe somewhere in the "Search in page text" section, so someone could just add a 2nd, 3rd, etc term, that would be pretty accessible.

Without this feature, "depicts" and other structured data becomes useless for typical users trying to find images with the builtin search using obvious search terms. I was adding structured data to some images and then wanted to test the search feature in other languages to see how it worked. It didn't work as expected, which led me here.