I have a Xiaomi and oneplus phone, neither of them have ever closed a background app so I dunno what you are talking about, but if phones are doing that then, yea fair enough thats a problem.
The wording in the linked website is talking more specifically about cpu limits, which is how most os manage background resources, whats the problem with that?
Sleep tracking is a good example you should use an event system, but developers are lazy and use "while (true) {}", which is my point.
I had a huwaii fit-bit-thing for a few months it uses two apps and I had issues getting them to talk to other software, but no problems tracking or shutting down, didn't change any settings. Maybe other apps have problems but theirs worked fine.
That’s a solved problem on iOS. iOS itself keeps track of measurements coming from your device even when it’s sleep using the power efficient Mx chip. Applications can then - with user permissions - request the data when needed. This has been the case since 2013.
The app doesn’t need to be running in the background.