I did some thinking about this, because the Bluetooth kit in my car doesn't have an unpair/forget function — but I realized I could accomplish the same thing by pairing it with a different device. (My car kit maintains only one paired device at a time.)
So I took a new iPad mini (A17 Pro) out there and paired it with the car kit to make it "forget" my iPhone 16 Pro Max. I then verified that the car kit was forgotten in the iPhone settings, too, and then reset network settings on the iPhone. When everything was up and running again, I tried forgetting the car kit in the iPad settings and paired the car kit with my iPhone again — and the iPhone still would not reconnect automatically when starting the car.
The new thing I learned during this process, tho', was that while the iPad was paired with the car kit, it did reconnect automatically. This now feels even more to me like an iPhone-specific problem, and possibly hardware-related?
I think I've mentioned this before, but it still seems important to me that if I have Bluetooth settings open on the iPhone when I start the car, I get a pop-up modal saying the car kit wants to pair (or connect, I forget the wording) and asking me to approve/deny. I don't think I've seen that modal on any other device, ever.