I’d have thought it was a good lesson. Pudding is a treat, if you don’t do as you’re told, no treat.
If there’s going to be consequence for her actions, then what would you have preferred she was denied? Story time, playing outside or something else entirely? Or do you not think it’s the nursery’s job to discipline?
Not saying you’re right or wrong, just curious.
EDIT: just read your other post, see you prefer time out. I suppose it depends what was said to your daughter first then. Not sure it’s worth being furious about, just tell nursery how you want it to work. If they don’t agree, choose a different nursery.