You’re indoors in the sense that you’re protected from the weather and the elements, and the cave could even have some kind of covering or entrance area that could be considered a door or doorway. People have built homes in caves.
Is caving an outside, inside activity?
Depending on the development of the spelunking infrastructure entering the cave might entail going in then outdoors again.
Indoors is an enclosed building, outdoors is everything outside of that