Not sure about the focus pop up but most/all of Apple’s other nags (like set up Siri, try Apple Music and the like) go away permanently if you go to the settings app and click “later” from there (as opposed to the button in the pop up which has the exact same label).
Google Play Store has a notification to enable notifications. You didn't read that wrong. It shows a badge and everything. I said no for years except that last time. Now I can't find how to turn it off again.
Can’t you just disable notifications for the Google Play Store app? Maybe it’s because I’m on GrapheneOS, but I can just enable/disable notifications like any other app.