Please see my comment above. You can use the language of gravitons and Feynman diagrams even for classical gravitational physics, but the calculations will be intractable for strong fields. See https://en.wikipedia.org/wiki/Graviton#Gravitons_and_renorma... for example

It's hypothetical, but less so than a lot of the things theoretical physicists consider.

Any quantum theory which reduces to general relativity in the classical limit will look like a theory of gravitons when quantum effects are small. This is just how the math works out in effective quantum field theories involving massless spin-2 particles.

I don't think its even a part of the standard model, still just a hypothesis.