What’s the downside to having one’s phone number in the public directory?
The difference is that an IP of a VPS doesn’t directly connect back to you. It’s in the provider’s name. Some providers let you change your IP address to a different one for a small fee.
It usually works well on Android. I use it on a few forums.
That’s the same with every Android app, though. When you’re not actively using your phone, some apps are put to sleep, which also stops their notifications. Very common on Samsung phones especially. You can usually add an app (or installed PWA) to a list of apps that you don’t want to sleep.