I am a little confused about the usual explanations about quantum entanglement.

In the Schrödinger picture, the state vector evolves in time.

In the Heisenberg picture, the state vector does not evolve in time.

In either case, there is no mention of the physical space, so the state vector is not dependent on space, clearly it belongs to an abstract Hilber space.

If it is not dependent on the physical space, it should be by definition a non-local object.

So why should we be surprised that something unrelated to space is connecting events that are spacelike separated?