So we know 31 Kingdom and now that 3 are Victory.
So presumably 316 + 31
And 23 Allies =
370, leaving 30 other cards* - either non supply? Or extra large Kingdom piles (maybe related to the rotating).
* being an even 30, I wouldn't expect any of these to be blanks
A number I found more interesting is 45 Action cards! So clearly, there will be some differently named piles too.
if we assume none of the treasures or victory cards are Action, that leaves 25 Action cards, so 20 more. If two piles are like knights, that's an extra 18. and the last 2 could be from those extra 30 cards somehow? Or some other similar mix.