Have you checked that your task hub name is different (needed when the share the same storage account) for your production function and the one in the staging slot? This is where the Azure function stores state for durable functions. If not, it is possible the following happens:
Your starter function in the staging slot is not picking up service bus messages because it is disabled as intended.
It starts the orchestration and the functions saves it's state in the storage account.
Here the issue happens if task hub names are the same: The staging functions can pick up work because it uses the same task hub name to save and check for state.