Fixes T11304. Prior to this change, we did an unnecessary write on every "*.search" call (this write didn't always actually write a row, since we only save unique saved queries, but still doesn't do anything useful ever, currently).
Instead, change this to not-write by default. We could add an "oh, and also I want you to do a write" option later, which would let us implement something like arc query-stuff which says "To see more results, view this URI in your browser: ...".
(It's possible to run one of these methods with an existing SavedQuery by using the key, so we still sometimes have a queryKey to return.)