Once the black tank got full the water backed up against the toilet flush gate.
At that point the water took the path of least resistance and traveled up through the gray tank and up the shower drain.
The water then escaped at the low point of the shower pan. (Which I imagine is lower than the top of the toilet bowl)
What this says to me is that your black tank filled, but did not overflow.
All (or the vast, vast majority anyway) of the water that escaped came through the gray tank.
"Water finds its own level", in this case the lowest point of escape was through the gray tank.
The fact that I am opinionated does not presuppose that I am wrong......