Make the field search do limits (whacks #17228) (#17283)

We're playing this whackamole because we added the middleware to universally sorta stomp on any `limit` or `offset` params, and they got stomped on. Which, in turn, led to my PR to make the default not limited. Which, in turn, led to the other issue this PR solves which makes the search things we relied upon to not have a limit, have a limit.