Roughly speaking there are two types of ##\psi##-epistemic theories. Adán Cabello calls them type I and type II ##\psi##-epistemic. There is also the names ##\psi##-statistical and ##\psi##-epistemic, which I'll use because I think they're more distinctive, but just note that many use ##\psi##-epistemic to mean both.
In the former the wavefunction is statistical in the sense of classical statistical mechanics, it is in essence a probability distribution over more fundamental degrees of freedom, hidden variables. In ##\psi##-epistemic theories however QM is not the statistical mechanics of some hidden variables. Rather it is just a general theory of inference for classical observables and you can't really recover the underlying reality directly from it, this is because all properties of the wavefunction just reflect generalised inference rules or normative expectations agents should hold. They're not related to "underlying/more fundamental" degrees of freedom.
As a direct contrast ##\psi##-statistical views would say ##(\psi,\phi) \neq 0## means that the two distributions ##\psi## and ##\phi## have some ontic states in common, where as in ##\psi##-epistemic views it just means that an agent who prepared ##\psi## should expect some chance to have a click on a ##\phi## measuring device.
Without going into much detail the PBR theorem essentially eliminates ##\psi##-statistical explanations that don't allow retrocausality or acausality. It says nothing at all about ##\psi##-epistemic views. Similarly retro/acausal ##\psi##-statistical and ##\psi##-epistemic views can escape the nonlocality conclusions of Bell's theorem.
The real force of the Frauchiger-Renner theorem and why it is causing interest in the Foundations community is because it seems to be the first result to say something about ##\psi##-epistemic views.
In the case of ##\psi##-statistical views something very definitive is being said of reality, it would just depend on the particular theory's hidden variables as to what that is.
##\psi##-epistemic views say that you can recover little about the underlying reality as so much of the QM formalism is simply "Agent-Reasoning" based. For example QBism says that the dimension of the Hilbert space (e.g. you need ##d = 3## for spin-##1##) reflects something as it seems to be agent independent. However they'd all basically say you can't really recover reality from QM, a new and very very different theory would be needed. QM will not turn out to be about ignorance of hidden more fundamental degrees of freedom. The most extreme view along these lines would be Bohr and Heisenberg style Copenhagen where the underlying reality has no hope of being recovered.