Capacitor 5.7.2 of Android, handleOnStart and handleOnStop do not seem to be called. We are reliant on these functions to perform certain tasks. For now, we can rely on handleOnResume and handleOnDestroy.
You mention version 5.7.2, was is working before and broke in that version?
I’ve used handleOnStart in some plugins and worked as expected, but have not tried in that specific version.
Do your methods have the @Override annotation?
If they have and don’t work, it would be good to report an issue on Issues · ionic-team/capacitor · GitHub and provide a sample app with a plugin where it can be reproduced.