I have shown here how the assumption that matter and geometry have the same fundamental origin requires the time evolution of a quantum state to differ from the Schrödinger equation.

This conclusion is unwarranted. It follows, not from the given assumption, but from the overcomplicated way that assumption is implemented and the kludges built on top of that. Here is how Hossenfelder introduces her central assumption:

What I am assuming here is then that in the to-be-found underlying theory, geometry carries the same information as the particles because they are the same. [...] Concretely, I will take this idea to imply that we have a fundamental quantum theory in which particles and their geometry are one and the same quantum state.

Taking this at face value, the quantum state of a universe containing gravitating matter is just a single ray in a Hilbert space. As cosmic time rolls on, that ray rotates. This unitary evolution of the state vector is the evolution both of the matter and of the geometry. There is, by assumption, no distinction between them. But Hossenfelder hacks one in! She says that the Hilbert space must factor into the tensor product of a Hilbert space for matter and a Hilbert space for geometry. And then she says that the only allowed states are tensor products of two copies of the same vector (up to a unitary that we could define away). If matter and geometry were truly the same, there would be no such factorization. We would not have to avoid generating entanglement between the two factors by breaking quantum mechanics, as Hossenfelder does, simply because there would not be two spaces to tango.

I am skeptical of this whole approach on multiple levels, but even granting the basic premise, it's a bad implementation of that premise. She doesn't have a model; she has a pathological "fix" to a problem of her own making.