Einstein's big mistake about entanglement was not taking into account how his own theory of Special Relativity completely modifies the way space, time or simultaneity would be experienced by something that appears traveling at the speed of light to us.
Einstein showed that all moving entities experience some time dilation effects, so time passes differently for each entity depending on its speed.
He also showed that different observers would arrange events in a different order based on their own motion, so every entity has its own idea of which events take place simultaneously, depending on its speed.
But Special Relativity also tells us that time would stop ticking altogether for an entity or process reaching the speed of light exactly, as its proper time would be zero and it would feel no time elapsed.
This means that every entity, process or phenomenon that appears to propagate at the speed of light to us (material observers) is "experiencing" a single blink of existence from its own point of view. So massless quanta (photons, gluons...) experience leaving and arriving at the same time, with emission and detection (and anything in between) happening all at once to them.
This is the first insight to understand entanglement: when the speed of light is involved, some form of instantaneity or simultaneity is also involved. What we call "the speed of light" is the way a group of instant relations among different spacetime coordinates maps into the subjective reference frame of a material oberver.
This is the true nature of any fundamental interaction we picture as unfolding at the speed of light: For the massless quanta and field disturbances that make up all the energy and information exchanges that take place in the universe, the different distances, durations, and sequences material observers create are of no use, since for them any distance is a point, any interval is an instant, and any sequence of events takes place simultaneously. The speed of light is, effectively, equivalent to teleportation, infinite speed, instantaneity or simultaneity.
This explains how entangled photons can show entanglement, even when their detections appear to be separated by large distances and time spans from our reference frame.
In the end, it doesn't matter how far apart in opposite directions two entangled photons appear to us, nor what specific sequence of events they seemed to endure for the time we think they were out there, nor which one appears to be detected before or after the other because, to themselves, all the spooky spacetime connections we observe are one and the same indivisible ensemble, where the common emission event and all related detections (no matter how scattered through spacetime) form a single and instantaneous action-reaction event with no spacetime qualities.
I cover the consequences of light speed being "infinite speed" at the same time in this article:
But if the speed of light is key for entanglement, then, how is it possible for some material particles to show entanglement at speeds other than c?
This is natural once we understand that any piece of matter is just a structure of fields, or a network of fundamental interactions, and that massless quanta and field perturbations do not propagate through spacetime at the speed of light, but are more like wormholes or "short circuits" that instantly interconnect different spacetime coordinates, always complying with the speed of light ratio.
So the light-like interactions that unfold each time form a network of instant relations that interconnect spacetime from past to present, stitching reality each time.
The true nature of entanglement has nothing to do with the subjective reference frame of any material observer, but with the pointlike and timeless existence that all the lightlike interactions spanning from a common emission event share instantly.
This is another key to fully understand entanglement: Entanglement, by the dual nature of the speed of light (understood as the instant simultaneity of all the events a massless quantum experiences for the spacetime interval a material observer experiences) underlies all physical phenomena, and is the fundamental principle that drives the universe.
Then, information or energy is not "carried" from place to place by massless entities at the speed of light. This is how we visualize it happens from our reference frame. But in fact, no property, entity, process or phenomena propagates, moves or evolves through spacetime, but is recreated from the patterns of instant connections that link the present moment with all past history of the universe, in the form of the entangled interactions that compose reality each time.
Material particles, and all their structures and properties (including their apparent motions at less than c or their entanglements with any other particles) are recreated before our eyes every time from the fundamental interactions that instantly interconnect spacetime fulfilling the speed of light constraint (not "propagating through spacetime at the speed of light").
So when we prepare a Bell experiment (be it with massless or massive particles), we are not creating the right conditions for entanglement to develop, we are creating the right conditions for the underlying entanglements composing the whole experiment to show up. Entanglement was always there, since it is the fundamental mechanism by which every entity or process exists in the universe.
So it is not that massive particles can show entanglement under some specific conditions, it is that entanglement underlies every structure or property material particles can display.
In the same way, entanglement is not a consequence of conservation laws, conservation laws are enforced because entanglement exists.
I describe in more detail how the instant (but lightlike) interactions that unfold each time underlie every physical phenomena that exists in the universe here:
https://quantumwormholes.medium.com/the-universe-explained-7df2cf8ced90
Hope you find it interesting.
