I do not believe a probation officer can give his authority to a police officer for a warrantless search of a residence. Probation officers can enter residences without permission for searches, have probationers arrested without warrants, and probationers can be held without bond until arriagned. The probation officer has to be present to do this type of a check. The cops can’t do it because the probation officer called them and asked them to do so. Maybe an attorney can correct me here.
I know a parole agent can authorize the police to search. It’s a condition of parole. Technically parolees are in custody.
Sorry don’t know about probation.