Jetpack Search Sidebar). Please make sure to configure some search filters for this widget, including a taxonomy filter: Tag, Category or Post Type.Checking a Tag, Category or Post Type filters the search results by the selected option.
Checking a Tag, Category or Post Type filter changes the query string, but does not alter the results.

This was happening because I had two Jetpack Search widgets set up - one in the footer, and one in the overlay. The code currently uses the first widget it finds in getFilterKeys():
In my case, it was using the wrong widget and so didn't have the full list of filters. This meant it did not react to any query string changes for post_tag and post_format, for example. The 'Clear Filters' button also didn't work correctly, only clearing the filters it knew about.
Two possible solutions to this:
getFilterKeys().cc @jsnmoon
Good catch, @bluefuton. I'll spin up a fix for this issue.