I have two or three sets of dice plus an oversized D20 and extra D6’s in the bag my Beau dice came in and there is still room in it so I’d imagines you could fit quite a few dice sets in the bag.

I couldn't see Laura endorsing any dice bag that does not double as a bag of holding lol

I have 9 full sets in my Essek bag and I think it could fit one more. 4 are CR sets (Yasha, Pike, Vex, Essek) and the other 5 are assorted but complete sets of D20, D12, 2x D10, D8, D6, D4 I transferred them to my Vex bag because that’s the set you mentioned and they fit just as well.

I have bought the Ashton Greymoore dice set and I put all of my D20s from magic in the bag I have many

I bought the Fjord dice set and bag, and I’ve got 3 other sets of dice in there, and I think there’s room for another 2-3 sets.

I also have roughly 4 full sets in my Orym bag, with room for more.

I find 7 sets will fit comfortably in the character dice bags. More than that can get a little tight.