Expect that soon enough they will ask people to put some colored sticker in their car, depending on the age of the car, the technology of the engine, and then you won't be allowed to drive "here" or "there" or you will need a super expensive "pollution-pass".
AFAIK - pre-2015 OnStar used 2G cellular radios which no longer work since we shutdown that cellular network a few years ago. You can check your VIN here to verify but I don't think you have anything to worry about: https://activate.onstar.com/en-US