"The second way to teach quantum mechanics leaves a blow-by-blow account of its discovery to the historians, and instead starts directly from the conceptual core -- namely, a certain generalization of probability theory to allow minus signs"

In my opinion, this is not the most natural and easiest way to get into quantum mechanics.

And there are also (undergraduate) physics books that tackle the quantum mechanical concepts directly, e.g:

https://www.feynmanlectures.caltech.edu/III_toc.html

especially:

https://www.feynmanlectures.caltech.edu/III_03.html (Probability Amplitudes)

Negative probabilities (Wigner Functions) are more advanced:

https://en.wikipedia.org/wiki/Wigner_quasiprobability_distri...

Lucien Hardy "Reconstructing quantum theory" is really conceptional, but I think it is not the best way to start.

https://arxiv.org/abs/1303.1538