I would assume it to be Uncommon, due to the fact that the Gray Maiden Dedication feat says "...You also gain access to special armor: Gray Maiden Plate..."
The phrase "You gain access to..." has, from what I have seen, been used solely in features or feats that grant you access to something of Uncommon rarity.
In addition it makes sense given its affiliation with a specific organization being analogous to things like racial weapons or Wayfinders. Also Gray Maiden Plate doesn't have a stat entry in the armor section or anywhere else besided this feat which is a little odd.
It could stand to be clarified, and likely will be in the final book, but I think inferring it as Uncommon is reasonable. If it was Rare you wouldn't be getting access to it without direct GM permission and it's obviously not Unique, and if it was Common you wouldn't have a feat specifying that it gives you access to it.
As an aside I wonder if we will get more uncommon armors and/or shields in the final book? Could be a good way to bring in cool classics like Dwarven Plate or specialized shields like the Klar (Though maybe that would be more like Exotic than Uncommon).
Lastly this actually raises a question on my part. Say you take a feat like Gray Maiden Dedication (Or say an ancestry feat that grants uncommon access), get your uncommon thing, and then at some point retrain the feat that granted it. Do you just keep the thing you already had but lose the ability to get more down the line? That makes the most sense as it would be silly to just have the thing poof obviously but I feel that opens the exploit of "Fighter takes feat to access uncommon weapon x that he already has proficiency in naturally, gets weapon, retrains feat to something he will use." Obviously this is something a lot of GMs might disapprove of but it certainly seems to be there. Better hope it doesn't break though cause you may not be able to get another. XD
