Android 13 has a setting, turned off by default, that allows one to
control devices known to Google Home without having to unlock the phone. Home device control was added to Quick Settings in Android 12 but to use it one first had to unlock their phone, even though the Lock Screen in includes a Home button. It always seemed silly to me to allow a user to put a button on the lock screen but not really do anything with it until the phone was unlocked.
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Per 9to5Google the search bar at the bottom of the home screen and the top of the app launcher in
Android 13 is supposed to be the same, but it has reverted to the differences that existed with Android 12. The unification has existed throughout the beta testing.
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