Is a bathroom considered a living space?

Yes. A finished bathroom counts as living space and is part of gross living area, the same as bedrooms, closets, and hallways. ANSI Z765 measures the whole finished floor instead of picking rooms, so every bathroom on an above-grade floor is in the total.

The same goes for half baths, powder rooms, and laundry rooms, as long as they are finished and above grade. A bathroom in a basement follows the basement: it is finished area, but it goes on the below-grade line of the appraisal, not into gross living area.

Bathrooms are also counted on their own. Appraisal forms list the number of full and half baths above grade, because buyers pay for them apart from size. So a bathroom shows up twice, once inside the square footage and once in the bath count.