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Geocoding is a non-trivial problem, and OSM's engine,Nominatim [1] isn't great.

There is not "an" engine used by OSM -- Nominatim is used by the application at OpenStreetMap.org, but I'm fairly sure OsmAnd does not use it.

OsmAnd used to integrate nominatim as an option (it was called "Online Search"). It worked okay. Unfortunately, that option has been removed.

Do you know a reson?