Patent agency is also the provincial intellectual property office, right?

No, it is an agency in China National Intellectual Property Administration, which is responsible for accepting patent applications and charging fees.

Provincial intellectual property offices belong to local intellectual property offices, and their main functions are to manage patent work within their respective administrative areas, such as investigating and handling counterfeit patents, handling infringement disputes, and mediating. Its superior supervisor is the provincial people's government, not China National Intellectual Property Administration.