I don't mean full, as in packed full to the brim. It is teeming with energy and virtual particles. There is no space that doesn't have energy and particles. It is a property of space itself.

Also yes, you could say space is nothing because it is an emergent phenomenon. But that is besides the point as pretty much everything in physics and therefore reality are emergent phenomena of more fundamental laws and properties. IE QFT pretty much says that no particles exist and its just all waves.

If you can properly explain gravity, step up and claim your noble prize. It is one of the most hotly studied areas currently in physics. Quantum loop gravity is a theory attempting to explain gravity at the quantum level by stating that spacetime emerges from quantum interactions.