"According to QBism, the wavefunction is no longer to be thought of as an objective measure of the probability of getting an outcome of a quantum experiment that two observers will necessarily both agree upon."
The wavefunction corresponds to probability (the Born Rule), precisely because squaring a Fourier Transform yields a "power spectrum"; accumulated energy per bin. Hence, when the energy arrives in discrete, equal amounts (quanta), then the accumulated-energy within each bin, divided by the quanta, yields the number of quanta per bin. In other words, it is a histogram (being inferred from a measured power spectrum), which is why the whole process yields probability estimates.
Rob McEachern