are the 4e Primordials personalities and behaviors more central to play than their cosmological identity in your campaign?
They are more important to them as monsters, yes. Imix, Yan-C-Bin, etc have histories and resonance in the game that predate, and extend well beyond, the 4e cosmology.
And there can be evil/amoral creator gods without the particular 4e set-up of Astral Plane, mortal world and Elemental Chaos.
The Raven Queen could be used in a game, as the good of death and fate, without using the Shadowfell. For instance, you could move Letherna to one of the poles of the mortal world, and the streams of souls flying there would be the Milky Way and St Elmo's fire.
what is the point of the different cosmological framing? If a unicorn is a unicorn is a unicorn regardless of it's origin, creature type, habitat, etc... what was the point of changing it?
Because the games use different cosmologies, both for reasons of flavour and of stakes.
In my last Oriental Adventures campaign, unicorns were celestial beings, members of the Celstial Bureaucracy. That game had no Feywild or Faerie - nature spirits live in the mortal world (in D&D terms, they live in "pocket dimensions" associated with their respective natural phenomena) and are also accountable to the Celestial Bureaucracy.
This different flavour supports different stakes in the campaign. In this particular case, those stakes ended up including ancient pacts reached between Heaven and the Lords of Karma.
So what did him being the "August Star of Heaven" mean? Was it intrinsic to his nature in the campaign world? And if not, why even bother assigning him a title?
It means that he is the son of Tou Mu, the chaotic god of the North Star, and that he has a place in her schemes, and in the series of unfolding events that are central to the campaign.
I'm asking what makes his unicorns distinct if they are the same with a different origin slapped on
I'm not sure they are distinct. That was my point - that what makes unicorns, or Graz'zt, distinct is not the plane they come from. So changing that plane doesn't ultimately change their character as monsters/NPCs.
Somewhat similarly, many of the same stories can be set in different "worlds" - Westerns, space operas, feudal Japan, Kung Fu fighting china, etc.