Storage costs are predictable and slow to accumulate. They are rarely the problem people are trying to address when they set a budget. As I said, storage would optionally continue to be charged at the normal rate, the other option being immediate deletion if you really need a super hard budget cap.
Once you get the alert that your budget is tripped you can go and see what's in storage via the console and delete it, only paying for a few hours of storage for things you don't want.
Once you get the alert that your budget is tripped you can go and see what's in storage via the console and delete it, only paying for a few hours of storage for things you don't want.