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?
It depends if the cave has a door.
Some people live in huts or other types of human dwellings that don’t have entry doors. They have doorways.
When I was visiting the Philippines I saw homes on stilts that did not actually have doors, but I would certainly consider the inside of such a structure to be indoors. Pre-colonial architecture may not use a front door.
I recognize this isn’t a great argument, but it’s arguable I think in principle.
If you don’t go in a door you’re not indoors.