Just because you're crossing public data with data you own does not mean you are not breaking the law.
Then on the other side, they have a database of cars that they sold and which are still under warranty - again, nothing about owners, none of the silo'ed personal information needs to be accessed at all. If the car is not on the "warranty==true" list, then they show the ad. I assume the ad doesn't display anything like "hey john smith, your warranty is expired!".
I mean, they probably don't even have that information for half the cars they scan because the warranty belongs to the car, not the person who bought the car. The warranty is transferred to the new owner if someone sells the car. They will not know the owner of all private used sales and used sales through 3rd party dealers.
Can the car license be tracked back to you? If yes, then anything attached to it is still personal. For example subscriptions or maintenance status.
Can they use this information to deny you access to their services if the subscription expires? Yes! Can they call you that it's about to expire? Probably yes. Can they call you about this other service? No way! Can they publicly shame you? I'd sue them.
Like I said, in the UK private companies are explicitly allowed to use AMPR machines to read licence plates(every supermarket in this country will have AMPR machines that record when you come and go). BMW just cross-references that with their own record to see if the car is under warranty or not - but like I said, they probably don't actually identify you in any way on the bilboard.
But surely, BMW also simply knows when they sold that specific car thanks to their own records, no?
Like, imagine you were selling cameras, you sold someone a camera and then they come in to your store 5 years later with the same device - is it ok for you to ask "hey, this device has an expired warranty, would you like to extend it?" - you know this because as a seller, you have to keep a record of every device sold. You don't even need to know the owner or any personal information about them - you just know that the camera in front of you has an expired warranty.
>> And the fact that you (the driver) have an expired warranty is private data.
Well I think that's where the problem lies. It's not the driver who has an expired warranty - it's the car that does, and there's nothing you can do, EU or not, to prevent BMW from simply knowing that a car they sold at point X only had a warranty for 3 years. They don't need to know anything about the owner at all.