tl;dr
Pros: Amazing space, tight but comfortable for up to 4 people. Phenomenal bath area. Gorgeous views. Private access off of main paths.
Cons: Not much privacy inside the apt, no closable door to the bathroom.
We would definitely stay here again.

The description of the apt does not do justice to it, it's much nicer. Upon arrival, you climb a short set of stairs to the "shared" balcony which has a partition separating it from the neighboring cave house. The view is excellent and is about a third of the way down the cliff face.

Through the front doors (one set glass doors for light and a set of wood doors for privacy, you enter the main room. To the left is a small, functional kitchen. The front section takes up two thirds of the room. Windows in the kitchen and by the door allow a fair amount of natural light in. There are two beds in the next section, one on each side, against the walls. There's a short half wall with big openings separating this space from the main bedroom space.

The back third of the room has a bed for two to the right and other furnishings at center and to the left. The door into the amazing bath area is to the left. The bath area is sunken several steps below the main room with that gorgeous tub centered at the rear of the room. The tub is in full view of the main room. The toilet is off to one side and the large shower area is off to the other providing some degree of privacy for each. Take a few minutes to figure out the set of switches controlling everything in the bath area. Some of them are interlinked (the ceiling lights turn off with the in-tub light and separately, for example).

There is also another balcony above the entrance to the cave house with chairs and an umbrella and a more open view but we were very happy on the main balcony.

The cave house slept the four of us (2 adults, 2 kids) comfortably and it has excellent WiFi in the front room and on the balcony. One caveat, the wonderful tub needs the pump running at all times which makes for a gentle burbling sound during the day that can sound louder in the silence of the night.

We arranged transportation to the apt through Rena which worked well. It's a pretty strenuous walk to the apt from the transfer point, but that's just what Santorini is like. Just be prepared for a lot of narrow steps. While she was very responsive, communicating with Rena in English was challenging.

Overall we had a great stay here. If we were to come back to Santorini, we'd stay here again.