How to get region informations for a given geo position

Hello,
I’m new in OpenStreetMap and want to use Nominatim to get region based informations for a given coordinate.

For example the coordinates of the town Sassnitz on the island Rügen:
https://nominatim.openstreetmap.org/reverse?format=json&lat=54.5157000&lon=13.644510

Is it possible to receive the island name “Rügen” for this geo coordinate?

Another example is the town Deggendorf. This town is a city in the low mountain range (Mittelgebierge, Bayrischer Wald)
https://nominatim.openstreetmap.org/reverse?format=json&lat=48.8408500&lon=12.9606800
How can i use Nominatim to extract informations like “Bayrischer Wald?”

The first question is always: is this information in OpenStreetMap.
For the name of the island, it probably is.
For the Bayrischer Wald, I doubt it, as this is a region without well defined boundaries.

Then if it is in OSM, you need to know how it is mapped. Rügen is probably not mapped as an administrative region, so it will not show up in the “stack” you get for a given coordinate (afaik).

So I fear that the current implementation of Nominatim cannot return the answers you are looking for.
Perhaps someone else will prove me wrong.

Bayrischer Wald is not found via nominatim. Rügen is found and mapped as island.

The object query at osm.org returns the island https://www.openstreetmap.org/query?lat=54.3832&lon=13.4245
Maybe this query can be done by Overpass?

Yes, Rügen is mapped and when you search for Rügen Nominatim will return the location of the island. But when you search for an address, Nominatim only returns administrative entities. It will never return geographic entities like islands, forests, etc.

Thank you! Yeah, I think I need both services . Fast reverse geocoding for locations and overpass for more informations about a region or a island. Can I use the same database for Nominatim and Overpass? i want to install both services on a single server

Here you can find reverse geo coding Technics on OSM
https://sathyasreek.blogspot.com/2018/12/reverse-geo-coding-using-open-street.html