If the problem can be fixed by rebooting or resetting the Ford head end, it's a Ford issue.
Any device that connects with the iPhone (or any other device) should never get into a state where it requires a reboot (or reset) to continue proper operation.
I've worked with Apple Support in the past when I've had an Apple device that would stop working and would only function properly after a reboot, and eventually those devices were fixed via a software update. (A recent example; an iPad would disconnect from a particular wireless network and any attempt to reconnect would fail until I rebooted the iPad - that clearly put the onus on it being an iPad issue.)
Given all this, it's clearly Ford's responsibility to diagnose and correct this issue.
(The same is true for other manufacturers' head ends that require a reboot or reset to operate properly.)
If you do an Internet search you will find myriad complaints about Ford's head end from both Apple and Android users.
Here is an example I myself experienced this past year:
I had been using CarPlay in a rental Ford without issue for multiple days in a row, but one day it decided it would not see the iPhone as a CarPlay device, just as a USB music player.
Nothing I could do would get the Ford head end to recognize the device. I tried different cords, I tried shutting the vehicle off, turning it back on, and nothing.
I finally gave up and went into a store.
When I came out of the store 45 minutes later and reconnected, the Ford recognized the device as a CarPlay device immediately.
I did not reboot my iPhone. I did not install an update to my iPhone. It was completely a Ford head end issue.
As far as your issues starting after a software update, that still doesn't mean the problem is Apple's.
The example I like to give is this:
Say a head end has a routine to add two numbers.
If the iPhone asks what "2 + 3" is, the head end answers "5," but if it asks for the total of "3 + 2," the head end answers "6."
If a software change causes iOS to always ask the total of "3 + 2" and it gets the wrong answer, it's not Apple's responsibility to go back to adding "2 + 3."