What area is used to determine the horizontal and vertical tail volumes of a vtail? What area is used to determine the tail volume of a 45 deg vtail?

Is the same entire area of the vtail used to calculate vertical and horizontal tail volume?

or do you use the projected areas in the x and y directions for horizontal and vertical tail volumes, respectively?

or other?
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.