We already provide a simple text search in #394 but a nice UI with some small buttons would improve this a lot.
Not sure how the UI should look like. qwant was doing it like this:

google:

... and once one of these icons is clicked we could just use the raw query like amenity:restaurant in the input field. I.e. the colon would then make the text special but ignore it if no coordinate is provided (?) Tricky.