Is there a standard definition of the "stall" phenomena? In the process of increasing angle of attack of a wing, lift is increasing to a maxima at a certain AOA, then decreasing as this AOA is exceeded.  This seems to be the current agreed upon definition of the stall point.

Yet the sharp pitch down and transition of the center of lift to 50% chord does not occur until the top lift pocket completely collapses.  Is this the true definition of "stall"?

There is also pre-stall buffeting as high AOA turbulence begins to affect the wing trailing edge.

So, are there really 3 parts to this that a pilot must understand, rather than just one?
The scientific definition of a stall is as you state in the first line, however in the cockpit that definition isn't actually that useful. Practically there's 2 parts of stalls a pilot needs to be aware of because they are things a pilot experiences, and impact the flying characteristics of the airplane:


Stall buffet: this isn't a stall, but it happens when you're very close to one. Recognizing a buffet may lead to a pilot decreasing AoA before entering a fully developed stall
Flow separation: when the flow separates from the top of the wings it may do so on one wing before the other, causing a wing drop, aileron input may work opposite of intent, and you of course have a high rate of descent. This can feel mild or violent depending on the airplane's characteristics and the speed at which the stall happens


Whether the definition of a stall is when the airflow separates or a change of the center of lift is academic, what a pilots needs to know is how to recognize the condition and recover.