Apple launders the location features of Apple Maps through platform location service controls. iOS will never, ever prompt you about Maps' own background location access. The controls for Maps' background location access are buried in System Services, and are defaulted on, and do not produce the tracking nag. The fact that the first-party Weather app is not also immune to the nag doesn't seem material.
The whole situation is in stark contrast to Android, where if you throw the phone in a drawer for a few months the platform will automatically revoke all of the privacy allowances of Google's own apps. Which is maybe not great, since resuming the use of such a device is sort of impossible (it will prompt you for shit like whether Phone is allowed to record audio), but you can't say it's anti privacy.
[EDIT] Though, regardless, I do see why it'd rankle that in fact Apple Maps ends up seeing fewer permission-reminders than Google Maps, even if it's for a not-exactly-intended-as-nefarious reason—I don't mean to dismiss your complaint.
Citation needed. I periodically get popups for even Apple's own first-party apps asking if I still want to share location. "Do you still want Weather to know where you are?" Yes, I do, because I use it. You may very well be getting the same message for Google apps, but that's not special anti-Google behavior.
> The other issue is the constant nagging, that can't be disabled, about iCloud backups being full
Then turn off iCloud backups. It's an optional feature that makes sense to be on by default, but that's trivially easy to disable if you don't want it.