The wave function collapse is quite real in that before measurement a particle interferes with itself and exists in a superposition, and after measurement it doesn't interfere with itself and is not in a superposition (from our perspective, at least).

Does the wave function collapse, or we get entangled with a specific outcome, or something else happens is subject to debate and is the substance of my question.

But "it acts as a wave, then acts as a specific point in space" part is quite real as it's what we observe in experiments.