The idealized gadget seen in the Penrose conformal diagram probably refers to a quantum of black hole or white hole. Often people refer to the truncated diagram such as the one below. In effect the entanglement is removed or ignored, and the entropy associated with that is defined by the entropy of a single black hole. The elementary diagram, such as the one I included yesterday, is an idealization. A real black hole has a massive entanglement with other states. I think the are with Hawking radiation and BMS symmetries that escape to ℐ^+, instead of with another black hole in a huge number of bipartite entanglements.
Susskind has this idea of ER = EPR, where Hawking radiation is entangled with black holes in a sort of wormhole manner. I think this is really with BMS charges and not so much with wormholes. The wormhole aspects from this stem from the local negative energy vacua near a black hole, say the Boulware vacuum, and the symmetries of this are taken off to ℐ^+ as ancillary symmetries of spacetime not found in i^0. So large astrophysical black holes are in a sense messy and we do not observe these entanglements and instead see a large number of separable states with thermal entropy.
LC