Apologies if this was mentioned already, but I’m surprised Obsidian Sync isn’t requesting to use iOS native “Background App Refresh” access to accomplish this. See for example that Obsidian doesn’t request this:
Whereas similar apps like Evernote do:
This isn’t bulletproof (iOS still algorithmically allows background access based on how often the app is used, battery impact and various other factors) but it’s the “right” way to do it on iOS.
I can’t speak to Android but I believe it offers similar APIs.
I’m not sure what underlying development platform obsidian is using but React Native offers this with APIs like react-native-background-fetch (react-native-background-fetch - npm) to do this.
Evernote is also a cross-platform mobile app, I believe written in React Native.
So I believe iOS offers some opportunity for this to be implemented for Obsidian Sync in a “native” way. This would apply to iCloud Drive sync which, as mentioned, handles background already at the iOS level.