The whole keyboard resonates differently tuned at 432 than at 440, the inter harmonics of the registers vibrate slightly different and it produces tones that you don't hear at 440 or you could say that in reverse I suppose. That said, 440 is clearer especially in the upper registers. I tune my grand piano at 438. My digital I can set anywhere I want. My aging ears are sensitive now and 440 and above penetrates my ears when set at 440 and 442. 438 takes the edge off, 432 can be really nice for nocturnes and such and classical era and older music.
It is said that the natural vibrations in the universe, on earth, in nature are 432 based. It harmonizes in the natural ( some folks buy into this and others don't). I create about 99% of what I play these days, I was gifted with this ability about 5 years ago, having always played other peoples works prior to that happening. Each tuning has me creating slightly different music pieces and on my digital piano, I run that through VST software that can give me the sounds of a C Bechstein grand, studio grand, or a Steinway D etc etc. Many different pianos including a set I bought of classical era pianos with old tunings not generally used today. I'll create different music, it plays on my mood by the sounds of these different instruments.
But there is a bird in our yard of many birds in our yard who comes to the window and chirps crazy loud to this one piano sound I have modeled on the digital, it's a K2 concert grand tuned to A 438. I haven't tried 432 to see what happens but it doesn't come and chirp when I set it to 440.
The idea that just the A note is affected is silly when tuning a piano. Middle A is the starting point to the entire tuning, not to mention there are different styles of tunings and these are all based off string beats. When you get good at tuning pianos, or at least good enough to hear these beats as you tune up and down the keyboard then you come to feeling that relationship between registers on the keyboard and even within a single unison. On a grand piano or any piano really, if you push down the sustain pedal all the way and hit any note in the mid range but A is common of course, you will hear all the strings of the keyboard set up a harmonic interchange in the background. These set up beats, that can be even or odd/uneven, so as you play the piano and use the pedal you can make some sweet sounds or harsh according to the actual tuning and how you feather that pedal in and out. It's a delicate part of the piano, that you don't get from say a flute or sax.
432 puts me right into the nocturne mood though and 438 is no slouch either. 440 changes my mood and hurts my ears at this age, especially in the upper registers ( I'm not talking about orchestral music but specifically my pianos in my living room). But 432 can get muddy in the deep base, string vibrations have slowed enough to get a bit murkey. I find 438 to be a nice all round tuning for me and my old grand likes it, the pins have to hold tighter with higher tunings ( my grand was built in 1898).
Other than that I don't have anything to say. I have no idea if the universe is in sync with 432 lol. I can see a sax played high as it plays one note at a time in the upper keyboard register of a piano, but has no complimentary harmonic vibrations to account for in the lower registers. If you tune the mid range @ 440, the upper @ more than a few cents higher, the lows a few cents lower on a piano keyboard the whole piano will sound out of tune, because it is. You can't go semitones or whole tones high or low across the keyboard, it would be unplayable. That said we do tune pianos with that slight push in the highs ( just cents not semitones) and pull in the lows or it will come out sounding flat or maybe dull is a better word.