The difference between the Avogadro Number and the new Avogadro Constant is that they will define it as a concrete integer value: 6.02NNNN... x 10^23. When the digits are agreed upon, I think the idea is that all subsequent digits are going to be defined as zero, making it a precise integer.
So then if it is a precise integer, we can then try construct objects with exactly that many particles (silicon atoms) and then weigh them, and so forth: masses can be tied to precise counts.
It's kind of analogous to declaring that an inch is exactly 2.54 mm: 2.54000000... not 2.5400XXX for some unknown X that is somehow empirically measured.
True, but it's defined relative to the kg. It's the quantity of Carbon-12 atoms in 12g of Carbon-12.
As for why it isn't an 'simpler' number, it's because if you want a standardized definition of something you have to have a reliable reference. Which is precisely why the kg itself is being redefined.
Side-note: the act of creating this ultra-pure kg of Si-28 has actually created a lot of useful science in its own right, which is nice.
Pull on one thread, and all the others may move.
Also of note with this change -- the amu will unlock from Carbon-12.
A "mole" is a unitless quantity. Literally it's just a number. I'm just dumbfounded that when they defined it, they didn't just pick an actual number but referenced an experiment to define it. Now it's a number.