You seem to still not get it.
Do you understand the term 'spacetime'?
It's like 'electromagnetism' which is a term meaning the underlying connection between electric fields with can exist with little in the way of magnetism and magnetic fields which can exist without much in the way of a connected electric field.
But when the two hook up together we have radio, light, Xrays, gamma and the like that makes up the spectrum of 'electromagnetic' fields.
Spacetime is like that except on a fundamental level time and space are hooked together and what you do with one you do to the other so a gravitational wave squishes time AND space, alternately a push in and out of the direction of travel and then a push sideways from the direction of travel, like a kid playing with dough, say two kids, one squishing the dough up and down and the other kid squishing it left and right. I don't suppose for a minute I got that totally accurately but that is the general idea. Maybe someone here with more knowledge can explain it better but the gist is, a gravity wave alters both space and time but the changes are so small you would never notice in a million years of having such waves go through your bodies and it was a hurculean scientific project to finally have enough sensitivity to reveal those waves of spacetime.
But why do you insist that space is not empty? OF COURSE IT IS NOT EMPTY.
But we are still in the midst of learning what space is all about and the best theories have not nailed it yet, like relativity, that describes the EFFECTS of spacetime like mass changing the flow of time and movement of mass changing the effects of space but that doesn't explain the underlying reality that creates space and time.
A new theory has to be invented which is not here yet. A new genius of the future may suss it all out in an overriding theory of the underpinnings of the universe but for now we have conjecture which is not even at the level of theory.
So news at 11.