I would like to eventually add OSM based local/POI search, but it will be quite a bit more complicated than using the simple Google API - but also much more powerful! It would probably work fine with a preset list containing relevant tags for search, but free form search would be most probably limited to advanced users knowing how the OSM tags work, given how the OSM data is structured. As for the other search options, address search is using Nominatim (so it is based on OSM data) and Wikipedia search goes over Geonames.