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?
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.