I installed Sidecar on Android now and looks like much is changed after this discussion. PWAs are now shown in the apps list inside settings, their battery usage, data usage, permissions etc are shown there. Their permissions are controlled from settings.
Also, when I was installing it, the notification area showed a wait bar from the Play Store saying “Adding Sidecar to the Home Screen”.
A tap and hold on the icon also shows you Site settings which takes you to a settings page where you can clear the stored data and can allow or disallow permissions.
