What area is used to determine the horizontal and vertical tail volumes of a vtail?
Depends on what the tail volume is used for.

For control authority and trim: Use the projected area.

For flight dynamics and damping: Reduce that by the cosine (horizontal) rsp. sine (vertical) of the V-angle, in your case multiply the projected areas by 0.707.

The control effectiveness of a control surface is proportional to the cosine of the V-angle, but the damping characteristics go down with the square of the cosine.