Yes, Bohr, and most physicists, are very confused on this subject, and do not properly understand Einstein's point. Physics doesn't even really exist anymore, because the term "physics" comes from Greek referring to the study of nature, but modern day physics is better described as "empirical mathematics." It is solely concerned with nothing else other than mapping what is observed to mathematical equations, and if you ask a more philosophical question of "okay, what do those equations actually tell us about the natural world?" it is typically dismissed. You see this with physicists like Lawrence Krauss and Niel deGrasse Tyson who dismiss philosophical questions as useless.

Einstein's concern was that he did not see them as useless but to want to talk about reality, and he understood quite well that special relativity is not "really" (in the sense of referring to reality) compatible with non-local influences since he had developed it. In fact, this was his motivation for developing general relativity to begin with. When Einstein introduced special relativity in 1905, it actually made no new empirical predictions, because it was mathematically equivalent to a theory Lorentz introduced in 1904.

Einstein's criticism of Lorentz's theory in Einstein's paper was that Lorentz's theory required a preferred slicing in spacetime, which Lorentz put there to take into account non-local effects from Newton's theory of gravity. Einstein argued that he believed this preferred slicing would later be proved to be superfluous, and after he published his paper, he sought to remove the non-locality from Newton's theory, and then subsequently sought to remove the non-locality from quantum mechanics, by fitting them both to local field theories.

It is quite trivial to see why non-locality is not "really" compatible with special relativity. Giving a definition of "realism" is quite difficult, but we can adopt a minimal, but not sufficient, criterion. This criterion is what I like to refer to as the "no solipsism" criterion. I experience in the world in a definite way, and so I assume you do as well, and how you perceive the world should not depend upon whether or not, or how, I look at you. Mathematically, this criterion is to say that relativity/variance should not bubble up to the scale of the mental states of human beings. The mental states of other humans should be invariant.

If you believe particles do not have real values until you measure them, then you can imagine a "Wigner's friend" type scenario where a friend in a lab measures a particle in a superposition of states while you are outside of the lab. From your perspective on the outside, you would have to describe both the friend and the particle in an entangled superposition of states, and thus the friend's mental state would not have an invariant and definite value until you look yourself, which would contradict with the friend's own experience.

You might try to "solve" this by arguing that when the friend first measures the particle, they "collapse" the state to a definite value for both observers, and so for the observer outside of the room, it's not in a superposition, but this is not quantum mechanics. Introducing such an invariant transition is called an objective collapse theory, and objective collapse theories fundamentally cannot be mathematically equivalent to quantum mechanics, because they break the linearity in the unitary evolution, and so in principle any objective collapse theory (like GRW theory of the Diosi-Penrose model) would made different empirical predictions to quantum mechanics.

Indeed, Bell definitively proved in 1964 that the states of particles simply cannot be Lorentz invariant given stock quantum mechanics, and since particles make up the human brain, then it logically follows that the mental states of observers cannot be invariant, i.e. you run into solipsism. You thus must give up one of two assumptions. You must either give up quantum mechanics, or you must give up special relativity, if you want to preserve realism.

Giving up special relativity, interestingly enough, does not actually require modifying the mathematics at all. It only requires introducing a philosophical asymmetry in how we interpret otherwise mathematically symmetric reference frames, by assigning one particular reference frame a privileged status of representing a "real" representation of the system, and all other frames as representing an "apparent" representation. This is known as a preferred slicing in spacetime, and John Bell discusses this in his paper "How to Teach Special Relativity."

You thus can actually fit quantum mechanics to a quite trivial realist interpretation, one where particles have real values at all times and merely evolve statistically, without modifying the mathematics at all, just by introducing a preferred slicing. But this is precisely what Einstein hated and was trying to avoid, because, like I said, his 1905 paper made no new predictions. His 1905 paper was really a bet: it was a bet that Lorentz's preferred slicing would be proved to be superfluous because gravity and quantum effects could be fit to local field theories, a bet which turned out to be wrong.

However, what Einstein did not anticipate is how little physicists actually care about reality and nature to begin with. Most physicists did not interpret Bell's theorem as proof nature is non-local and therefore a preferred slicing is logically necessary. Most physicists just argued that we should stop talking about "reality" at all and only talk about what is consciously observed by the experimenter, and predicting that is all that matters, and if that is all you are concerned with, then there really is no incompatibility between quantum theory and special relativity.

Einstein was baffled by this and once even asked Abraham Pais, "do you really believe that the moon doesn't exist when you aren't looking at it?" This is what I mean by saying physics no longer exists. Physicists often lie to your face. When they talk to Laymen and try to explain things, they will often give realist explanations, like describing vision in terms of photons reflecting off of a surface and being absorbed into the retinas of our eyes, or describing virtual particles as a "bubbling brew of particles popping in and out of existence," etc.

Pretty much any time a physicist gives a realist explanation of something to a Laymen, they are lying, because these things literally do not exist in the theory. Objectively, quantum field theory does not anything with any definite properties at all. If I walk to my living room to my kitchen, I will feel quite strongly that I traversed a definite trajectory from my living room to my kitchen, and thus the particles that make up my body should have also traversed such a definite trajectory.

But such a definite trajectory for the particles literally does not exist in quantum field theory. This is why John Bell described modern physics as a kind of "radical solipsism," because everything you perceive and all your memories have to be taken to be a lie, because they don't actually exist in the physics. Only the most direct impression in your conscious experience does in the immediate moment of observation.

A lot of students who first start learning physics don't understand this and thus remain in denial of it. They genuinely cannot fathom the absurdity that modern day "physics" merely describes predicts what is consciously observed in the moment and gives no underlying realist account of how what was observed came to be to begin with, and so they deny it by regurgitating certain statements they've heard through the grapevine, like that there is a "collapse" or something about "branching" that explains this, but when you actually learn more and read the academic literature, once go beyond the Dunning-Kruger effect, you will start to learn that these "explanations" don't actually give an underlying account of what we observe at all (John Bell debunks the "collapse" argument in his article "Against 'Measurement'" and the "branching" argument in his paper "Quantum Mechanics for Cosmologists") and that modern physics simply does not have one.

This is what bothered Einstein so much. You must necessarily either give up quantum mechanics, or you must introduce a preferred slicing in spacetime, thereby giving up "real" relativity (whereby relativistic effects are then interpreted to be only apparent), if you actually want a realistic account. If you insist upon not modifying the mathematics of quantum mechanics at all, as well as not introducing a preferred slicing into special relativity, then when you combine the two, you inevitably run into solipsism, because you cannot have a logically consistent accounting of reality whereby each observer's mental state is invariant.