Is the wavefunction a physical quantity?

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Or is it a physical property of the quantum system? Or else?

The Joint Committe fo Guides in Metrology:
http://www.bipm.org/en/committees/jc/jcgm/
says that:
"A physical quantity (or "physical magnitude") is a physical property of a phenomenon, body, or substance, that can be quantified by measurement"

But I don't know how to extrapolate if the wavefunction is it or not...

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[Nugatory]

There's no really satisfactory answer to your question, in part because there is no really satisfactory definition of what a physical quantity is (a definition that links to wikipedia is no definition at all), in part because the mathematical formalism of quantum mechanics doesn't give much of anything except probabilities. However, it is very hard to imagine any definition of "quantified by measurement" that could be applied to a wave function... so the not really satisfactory answer to your question is "No".

You might want to try googling for "PBR theorem" though.

I'm going to close this thread now, not because there is anything wrong with the question, but because moderating the discussion is going to be a lot of work with no happy outcome an internet forum is poorly suited to discussing it. As always, everyone is encouraged to PM me or another mentor if they would like the thread reopened so that they can contribute.