I searched both treasuries and I can't find the ring or the bag.
Only found some gauntlets of fumbling.

IIRC, they are on the floor below, in a room impossible to open from the outside (frozen door). You have to speak with the portrait to be teleported there, after killing the boss.

What you are searching for is "Nathaniel's Holding Bag".

Yea, I accessed one room via the picture and the other by manipulating the prism mechanism.
Couldn't find anything in either room. Will try restarting.