What is the space time fabric made up of?
The space time fabric is a mathematical abstraction which doesn't exist as such.
General Relativity (GR) describes spacetime in terms of Einstein's field equations.
This apparently simple equation is actually ten second order partial differential equations which describe the shape of space time. It describes how matter, energy and momentum cause space time to curve. As the mathematics is hard, analogies are used to explain GR in simpler terms.
Many think of the universe as a bag of stuff. It isn't. The rubber sheet with balls causing indentations is often used to describe gravity. It is quite a good analogy, but it isn't what really is happening. When we say space time is curved it is natural to think in terms of something physical bending. If space time has a physical fabric, then we would be able to measure absolute space and time relative to that fabric. The Michelson-Morley experiment proved that this does not exist.
What GR actually describes is a four dimensional "space" with three spatial dimensions and a time dimension. This four dimensional "space" has no structure. It is simply a mathematical abstraction to explain how objects move in four dimensional lines called geodesics.
On very small quantum scales space is full of virtual particle - antiparticle pairs which spontaneously come into existence and then annihilate each other. This means that energy is everywhere.
What the GR field equations actually say is that the shape of a region of space time is defined by the mass, energy and momentum of things in the region. If anything the fabric of space time is energy itself. The shape being defined by the form the energy takes.
One of the major problems physics faces is that GR and quantum mechanics are incompatible with each other. We need new physics to unify them. Such a new physics may reveal an underlying structure.