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Einstein's relativity both special and general is only concerned with the limitations on measurements with real light and real massive particles used as signals. Entanglement signals do not need real light or real particles in their direct communication link channel. The real particles only play a role locally in the detection physics.
Entanglement signals are non-metrical linking arbitrarily possibly widely separated irreversibly recorded detection events. In the case of special relativity there is a unique global spacetime separation between them. That is not really useful because spacetime is curved and there is no path-independent measure of global separation.
Suppose Alice and Bob have entanglement signaling capability. The obvious protocol should be for each to note their CMB temperature from the Big Bang as well as their peculiar velocity relative to the Hubble flow as shown by departures from isotropy of the CMB. They can also note what star system they are in.
Other than that, there is no conceptual clash with relativity. Entanglement signaling is a global topological effect independent of metrical constraints and consistent with them.
Alice and Bob can communicate across time, both forwards and backwards.