Hey, James Douglas talked to me about search APIs. I started an overview of what's available at
mw:API:Search_and_discovery that links to existing API pages and the generated MediaWiki API help. In particular the API pages have a link to [try in ApiSandbox] so you can load them up and play around with the MediaWiki API search modules. I added a link to this overview on your team's top-level
mw:Search and Discovery page page.
I'm also writing articles for a planned "Data and developer hub" to encourage third-party developers to use Wikimedia data and APIs. Fortuitously two of the early articles are about how desktop and mobile use search, "Page info in search results" and "Showing nearby wiki information", so API:Search and discovery links to these as well.
Though I'm on the Reading team I'll do what I can to document your stuff, particularly what it can do for third-party developers.