Remove updatePublicMode from StatusBar.java

There is still one place where status bar needs to notify
NotificationLockScreenUserManager to updatePublicMode (for the
notification showing sensitive info bug).

Otherwise, this commit removes udpatePublicMode from StatusBar and
should have the exact same call semantics as before.

Test: `atest SystemUITests`
Bug: 112656929
Change-Id: I4fe6bc1d6519ae12581f3c17f14c2fcb505eb5f5