Art 440 does tell us how to determine conductor size and overcurrent protection settings, but mostly applies to other then the factory assembled units we commonly find in the wild. If you were to look at each component and figure these values out yourself you almost always come up with what is on the nameplate though or very very close, so you are right - the manufacturer did the math for you.
Correct, it is a listed component, all you need to do is follow instructions and provide minimum conductor size and overcurrent protection according to what is on the nameplate - even if the internal breaker is a 60 but the nameplate calls for a 25 - then 25 is the required protection for your supply circuit.
One thing code doesn't mention when it comes to how much starting current a compressor may draw is the reality of impedance in the supply circuit. If POCO has a small transformer, you have long service conductors, long feeders, long branch circuit conductors or any combinations of those - LRA marked on the unit may never be reached.
I kind of assume the LRA value marked on the unit doesn't figure on any voltage drop when in a LRA condition. Max OCPD may factor in possible drop in voltage IDK, I know many breaker manufacturers would recommend a higher trip setting for a motor with same rating as many of those compressor units, but reality in most instances is that the LRA is limited by circuit and or source impedance and the devices usually will hold at the levels mentioned on the nameplates.