Or in the increasing number of public spaces that are privately owned. If advanced facial recognition is being used, does it really matter who owns the cameras? Especially once that data is put up for sale...
Not really, no. If it's in a shop, it'll be operated by the shop. If it's in a supermarket car park, it'll be operated by the supermarket. If it's in a public park, pedestrianised street, or government building, it'll be state-operated.
Bear in mind that the vast majority of those cameras are privately-owned (i.e. shops, homes, etc.), not operated by the state.