Not familiar with your layout but most showers drain into the gray. You use a lot more water at the bath sink than you think and it probably
does go into the black tank. The average person uses 5 times more water washing their face at the sink and 3 times more water brushing teeth at the sink than you use for one flush of the head. Not suggesting you wash your face and brush your teeth in the toilet.
You can call the 800 number and get a quicker response.