Ideas
Also having this issue with at least one older save. Didn't have the issue upon trying a new save.
I normally play with mods, but I took everything out, deleted the localthumbcache file & resource.cfg file and tested it vanilla/no mods. I also tried repairing my game, and had no luck. All the same issues as OP. New save files are there are no issues, but old files I can't drag from storage to inventory.
This makes the game unplayable for me. Please fix ASAP.
Follow up to this. I started a new save shortly after this post awhile back, and now that save is having the same issue. I don't know what is triggering it other than maybe the amount of stacks (or items?) in the storage?
EDIT: Please, fix this as soon as possible. It makes collecting/using items borderline impossible.