Is it possible to get a dataset of administrative boundaries available in OSM?

I am relatively new to OSM and understand that you can access administrative regions by their name; for example, this overpass query

way(area.a)["highway"]; node (w); out body;

gets all nodes on highways in Gaithersburg, MD. Under the hood, I assume there is some kind of key-value store that maps words (e.g. Gaithersburg) to their respective areas.
My question is, is it possible to access a list/dataset of all administrative boundaries in an area, such that an application user could select one from a menu and seamlessly query inside that boundary?

It is possible but unless you’re talking a very small area, probably
beyond what Overpass can do for you. The most performant solution is to
import osm boundary data into a PostGIS database with osm2pgsql - you
can limit the import to admin boundaries - and then run queries on that,
like “give me all polygons and names for adminlevel=2 boundaries (that
would be countries), or “give me all adminlevel=4 boundaries inside this
particular adminlevel=” boundary” and so on.

There used to be a web site called “OSM Boundaries” that would give you
pre-made boundary data sets, but that has crashed and someone is trying
to re-build it here but it says it is still
“in alpha stage”.