Once API calls are locked you can open the console, disable all the things that caused you to hit your budget, and then raise the budget a bit to get access to

Once API calls are locked you can open the console, disable all the things that caused you to hit your budget, and then raise the budget a bit to get access to the storage APIs again and manage your storage. Or, the console's storage browser should let you browse and delete files as well. And again, there should be an option to delete all storage immediately for a hard cap on your budget if you really want that.