Not sure about Gridfinity compatibility, but there is an underlying 25mm grid for the storage units (my OCD demanded I ask after that already). That said, I did already just pitch mine in a plastic storage organizer:
(the square ones — I wish the rectangular ones can in a front–back divider design)
though maybe a foam insert would be better, or maybe I’ll try cutting out the holder in some HDPE.
EDIT: Actually, the 8 clamps fit perfectly in: