You have your phone set wrong and/or over thinking what you need to do.
You do not have to keep it running in background. You can kill it.
You need Location Always (Precise) and Background App Processing. That’s what background App Processing is for.
iOS will relaunch the app in background and you will NOT see it in your list of recently used apps. It will still appear as shutdown.
If you look at Battery usage you’ll Apps Background usage. I kill the Tesla App all the time. But you’ll still see it is consuming some resources. You’ll see another app in the list below consuming resources in background.
I wrote it and I had to understand how it works. Even if I kill all apps and reboot my phone and not touch either app they will still work.
You will get warnings from iOS on Apps that behave this way because some users don’t realize they have apps that are consuming resources (because they can be invisible) And will ask if you want to continue allowing it.
If you start the app and background it or kill the app and let the iOS restart it is essentially the same thing. It still needs permission to operate in background if it’s not in foreground.