[SettingsProvider] update ringtone cache only after setting is update

Previously RingtoneManager may override the ringtone cache even when the
ringtone setting is not updated. This CL moves the cache update logic to
SettingsProvider, and only updates the cache if the setting itself has
been updated.

BUG: 280219393
Test: manual with work profile creation
Change-Id: I63ce56ef0cbfb8862ffbb56d7137a0f0223110a2