Using Shortcuts, a user can use the Cloud model via Private Cloud Compute, the Cloud Pro with "world knowledge, and the on-device model. It occurred to me I probably don't need the Cloud; I switched to the on-device model, which worked fine.

There's no way for Siri or anybody else to know anything about a transaction using Private Cloud Compute:

    We designed Private Cloud Compute to make several guarantees about
    the way it handles user data [1]:
    
    A user’s device sends data to PCC for the sole, exclusive purpose of
    fulfilling the user’s inference request. PCC uses that data only to
    perform the operations requested by the user. User data stays on the
    PCC nodes that are processing the request only until the response is
    returned. PCC deletes the user’s data after fulfilling the request,
    and no user data is retained in any form after the response is
    returned. User data is never available to Apple — even to staff with
    administrative access to the production service or hardware.