Quantum mechanics is a local theory, if it was not we could not combine it with special relativity, where locality is a requirement. A lot of the talk on QM is confused because literally in the mathematics there is no superluminal effects (the No-communication Theorem), but people always speak of it like there is nonlocality. QM ends up being discussed in a way where it has a kind of pseudononlocality where there are nonlocal effects but that nature conspires to hide them from us.
We see this with the traditional way that the EPR paradox is explained: when Charlie sends Alice and Bob particles in an entangled pair, he's not really sending them particles, but a giant wave that connects the two, and the moment Alice measures her particle, that wave "collapses" on both ends simultaneously for Alice and Bob.
If, somehow, Bob could see the wave without collapsing it, that would indeed superluminally signal Bob. But then it's stated that it's impossible for Bob to see the wave, any attempt will just collapse it himself. So, in a sense, the claim is that there are superluminal signals, yet nature conspires in a way to always hide them from us just below the surface.
I think we should be cautious to propose there is some sort of conspiratorial nonlocality that is hiding just below the surface. A much simpler explanation is to just say that when Alice makes a measurement, she is merely only updating her prediction as to what she will see if she were to go measure Bob's particle in the future, rather than stating that she is describing something about what Bob's particle is doing.
In Carlo Rovelli's paper "Relational EPR," he points out that the difficulty people have with truly embracing that QM is local is that we have a tendency to ascribe a sort of cosmic reference frame to the universe implicitly, without even realizing we're doing it, despite such a thing violating the laws of physics.
We like to imagine that our own reference frames are "subjective" and that "objective" reality consists of some sort of cosmic observer that can see everything simultaneously. However, such a thing is not only incompatible with quantum mechanics, it's not even compatible with special relativity as such a thing would require a preferred foliation in spacetime.
In our heads, we like to imagine that when we snap our fingers, it is meaningful to talk about what is happening for some species living in the Andromeda galaxy in that very same moment I snapped my fingers, as if there is a simultaneous "now," but such a thing cannot exist. You cannot have some sort of cosmic observer that sees everything simultaneously.
The problem is, when you point this out, people want to throw the baby out with the bathwater. They think that because our notion of objective reality is flawed and quite literally not compatible with the laws of physics, we should just throw out the notion that there even is an objective reality. Some others may refuse to let go of their preconceptions simply because they're afraid that letting them go means we have to abandon the notion of objective reality.
Yet, that's not the point at all. The point is not that we should abandon the notion that there is a reality independent of the observer, but we should abandon certain metaphysical assumptions about what constitutes that reality. It simply cannot be some sort of third-person godlike point of view that sees everything at once. There is no reason for one reference frame to be preferred over any others, nor is there some reference frame where you can acquire all information about the universe simultaneously.
Instead, we have to reinterpret reality as reference frame dependent, i.e. that reality just is the totality of the different possible frames of reference as these describe how things relate to everything else. These do not need to even be conscious observers, you can write down the equations describing things from the "point of view" of even a rock and trace out that reference frame, for example.
If you stick to this, i.e. you stick to only tracing out reference frames and not trying to posit some sort of cosmic observer that can simultaneously see everything at once, then any difficulties explaining the EPR paradox locally disappear. The nonlocally is artificially constructed by positing some sort of nonlocal superbeing which can see both Alice and Bob's particle states simultaneously, which can't physically exist.
Even if there was a third-party observer between them, they too would occupy a frame of reference whereby information can only reach them at the speed of light and no faster, and so if you trace out their frame of reference, you don't end up with any contradictions or anything even apparently nonlocal either.
The reason for this bizarre and conspiratorial pseudo-nonlocality is therefore a result of us artificially adding in a metaphysical construct which doesn't even make sense.
