the rental car computer can store your data. Contacts, etc. This is one of the many reasons I don't like smart phones. I use an old fogey flip phone with buttons that only makes phone calls.
About a year ago, WaPo published an article about phones and rentals. They were assisted by a white hat hacker. They rented a car and extracted data for SEVENTY past renters. I didn't find that article right away, but I found this below. Sounds like the same project.
https://protectme.blog/devices/connecting-your-phone-to-a-rental-car/
"After hacking into an infotainment system they discovered:
unique identifiers for previously connected phones;
detailed log of phone calls;
text messages;
photos; and
and entire contact lists including other peoples names, address, and emails."
A black hat hacker could rent a car for a day and get a trove of data.
This is a related article on WaPo:
]https://www.washingtonpost.com/technology/2019/12/17/what-does-your-car-know-about-you-we-hacked-chevy-find-out/
"Among the trove of data points were unique identifiers for my and Dougs phones, and a detailed log of phone calls from the previous week. There was a long list of contacts, right down to peoples address, emails and even photos."
Be wary about pairing a phone with a rental car. Once you return it, it still holds your data. I bet there's something in the rental contract fine print about this. Maybe not.
This isn't even a free service, but:
"If the service is free, YOU are the product."
We are all data mines for the monetizers.
Play the radio. Use the phone when you're not driving.