We had a bunch of issues when we moved my spouse from her android to iPhone11. I've had an apple phone since day one, and never experienced any issues with Bluetooth.
Her issues were primarily car connect problems, and it seemed to occur in either my 2020 Jeep, or her 2017 Veloster, where the android device worked fine.
We both have model 11's of the phone. I have the pro, she has the non pro. For me it was get in and go. Just had to remove the iPhone X profile and add the 11. For her, it would not work. We tried everything mentioned in this forum, but I could not get anything stable expect car play, which works great with either device. In the end, I removed all settings (phone stuffs) from the Jeep, then reset the entire Uconnect system inside the vehicle. Following that, I removed the battery terminals for 15min, and that did the trick. No more issues. Why? Who knows.
The Hyundai was the biggest issue, but the easiest to fix. There's the typical menu option where you can add/remove the phone, and another menu option for Bluetooth settings. Because we cleared her old android phone from the system, those secondary settings reset to default. It's critical that those settings be changed in order for the phone to connect when you first start the car. Not sure if this applies to all Hyundai vehicles, but these changes enabled her to use the phone in both autos without issue.
For those with other types of cars/trucks, it may be worth while digging around in your menu screen to ensure there are no hidden BT options.
Aside from that, ensure that all BT devices are removed before you start and while it probably does little, try to reset network settings on the phone.
Bluetooth is an evolving standard that changes every few years. The newest iphones have the latest implementation of this technology, whereas car manufactures take longer to update. Even a new 2020 may have a older Bluetooth chip on board, and certainly that 2013 model will be even older. As the spec evolved, so did the speed, and capabilities. While they claim backwards compatibility where the iphone 11 should be able to connect to say a 1.0 spec, its not always that easy. There are over 30 thousand members on the BT list, and that makes for a lot of different devices on the market. I have a Sony smart speaker from 2008 that uses BT 2.1, but its just not 2.1 that could be the problem, but also any BT chip that has energy saving features. I can use my old S3 from Samsung with that Sony speaker, and my iphone 5 works ok as well. After that, none would work, including my wifes old S5 from Samsung. While none of this should apply to the latest gadgets, especially airpods, it would certainly apply to automobiles.