Organic Maps is the most private offline map app, it looks prettier than Google Maps and Apple Maps, it leverages data from openstreetmap that you can update easily compared to the competitors, it’s very battery efficient and the best of all its FOSS.
OSM search is actually really, really bad if you don’t use overpass. This has nothing to do with data quality. The default search just sucks. Organic Maps is no different here. You simply cannot throw a basic string search at a relational database and expect good results.
True, would something like Elasticsearch work better? What is Overpass?
I have no clue about Elasticsearch, but Overpass is a very advanced search and filter interface for the OSM database
https://overpass-turbo.eu/