TL;DR: Does the Celestial Armor require medium armor proficiency?
But, does it work just like a Chainmail made from Celestial Mithral, which then makes the armor light enough to be considered as light armor, but still requires medium armor proficiency? After all, it does seem to be made from it, even if it doesn't state it.
When checking other armors, I found the Elven Chain which state that it is a Chainmail, but should be considered as light armor, even from the proficiency point of view. But it also state that it is made from Mithral unlike the Celestial Armor.