Export hierarchical structure of (administrative) relations

I'm looking for a way or tool to get a list of all type=boundary, boundary=administrative relations and their hierarchical structure (relation A has children B and C and B has children D and E and so on...). So something like: all boroughs of Berlin, Germany and all localities of all the boroughs of Berlin, Germany (Wikipedia).

Basically, I only need the osm_ids.

I tried using the Overpass API (https://overpass-turbo.eu/s/1aVA) but unfortunately it's very slow and I only get the immediate children. Now I could make a request for each of the children and get their children etc, but it takes forever.

Is there any good tool or way to achieve this? I'm sure I'm not the first to need the hierarchical structure of relations.