general relativity - String theory and one idea of "quantum structure of spacetime"

First of all, I do recognize that I haven't studied string theory up to this point. I'm actualy just getting started with it.

So my question here is as follows: Einstein's theory of General Relativity basically says that "gravity is geometry of spacetime". That would be a very rough idea of what it is all about. The gravitational field isn't something propagating on some background, it is the background itself.

Now, string theory is said to have the potential to be the so sought theory of quantum gravity. One way to support this claim is that a massless spin 2 particle appears naturaly in the theory and this particle could be thought as the graviton. Historically it seems this particle was what motivated string theory to be used for quantum gravity and not for hadronic physics.

It is also said that string theory has the potential to be a theory of everything, unifying the four fundamental forces and all the particles in a single description.

Now, with all that said, here comes the question: it seems to me, that having in mind the basic idea of GR that gravity is the geometry of spacetime, any theory of quantum gravity should also be a quantum theory of spacetime.

Now, in string theory, as far as I know, one studies (quantum) strings, propagating in a fixed background (usually taken to be either Minkowski Spacetime or AdS spacetime) and then it ends up describing a graviton.

But how can this be a theory of quantum gravity, or even a theory of everything, if it is not a quantum theory of spacetime? In other words: spacetime is a fixed background as far as I know. Furthermore, one could interpret the graviton field as a perturbation of the background, but not all spacetimes are small perturbations of Minkowski spacetime. Actualy, I believe that at the Planck scale, where quantum gravity would be needed, it certainly wouldn't be the case that spacetime is a perturbation of Minkowski spacetime.

So my question is: how does string theory deals with this? It doesn't provide a quantum description of spacetime? If so, how can it be a true quantum gravity theory and how can it be a theory of everything?