I'm not sure that "helps" is the word. As far as I am concerned, that change in wording would totally move the goalposts, and goes quite I way to explaining why I was getting confused by what you've been writing. "A given power output" is very largely dependent upon the load, and could be dramatically less than the "rated power" (which is the maximum output power it is designed to be able to provide.I don't see the problem. That's exactly what it means. Change it to rated power if it helps.
However, I think I'm coming to understand what has caused all the confusion, even though it still leaves me with one big question.
As we know, the rise in motor speed when one increases voltage from, say,380V to 415V is trivial, typically 0.1% - 0.2% for all but the smallest motors - and if the load is constant and we assume that (actual) power output is roughly proportional to voltage squared, the increase in (actual) power output is also trivial. The situation is therefore that of an (actual) output power that remains essentially unchanged when voltage rises from 380V to 415V - and if we assume unchanged efficiency, that also means that the (actual) input power to the motor remains essentially unchanged when voltage increases from 380V to 415V.
If input power remains unchanged when voltage is increased, that obviously must mean that current (and/or PF) has reduced, and it is that reduction in current that you have been 'majoring' on.
As you've been saying, that reduction in current is 'anomalous' 'in terms of what one would expect (from Ohm's Law) with a resistive load, or even a 'simple inductive load'. What I am struggling with, in the case of a motor, is the mechanism of the reduction in current (and PF).
On the face of it, I would have thought that the only things which the motor 'knows about' are the load, its speed and the supplied voltage. If the first two remain essentially unchanged when voltage is increased, what is the mechanism whereby the current and PF reduce? I'm clearly 'missing something', but obviously don't know what!
PF has brought itself 'into it' to an appreciable extent. Just looking at one typical example from your catalogue (the "315 SMA" motor), when voltage increases from 380V to 415V (an increase of about 9.2%), motor speed increases from 1486 to 1488 rpm (and increase of about 0.13% -so' essentially unchanged'). With the increase in voltage, current decreases from 200A to 189A (a reduction of 5.5%), and PF reduces from 0.88 to 0.86 (a reduction of about 2.27%). It is the combination of that 5.5% reduction in current and ~2.3% reduction in PF that means that power remains essentially unchanged despite the (~9.2%) increase in voltage - with the figures given, the power input is 66,800 W with 380V and and 67,454 W with 415V.There's no need to bring PF into it, but a reduction in PF causes the current to rise (for a given power).
However, as above, I still don't know enough to understand the mechanism of those decreases in current and PF, despite essentially constant load and speed.
Kind Regards, John