Do cars have SIMs inside them that have free 4G/5G access and can send information that way?

Yes, most modern cars do. At the very least those with Infotainment systems. They pull updates and traffic data that way (and a bunch more).

I know we are in a privacy community here, but i personally would question what you are trying to do here. Don't get me wrong. Staying away from Tesla and other Companies that are trying to sell heated Seats as a Service with a subscription to wipers or such is certainly a great idea. But beyond that, i don't think there's too much to worry about. My 2022 Kia Ceed has a build in Infotainment system and some sort of internet connectivity. And if Kia wanted to, they probably could track where i drive. But at the point where you are carrying a phone, i'd worry much more about that than about my car. Ripping out Radio antennas probably doesn't do a whole lot. And depending on where you live, emergency location information provided by the car might be mandated by law. Skipping infotainment systems also might not help. Most manufacturers build more or less one trim level and enable/disable features you pay for. They might not bolt the display in, but the Computer behind it is probably still there to some extend.

At least in the case of Kia i haven't found anything in their privacy statement that suggests they are collecting data from the car beyond what they read out when you bring it in for service. I'm no lawyer and am not sure if they have different privacy policies depending on the country you're in, but it's good enough for me.