Lift the Playlists module's shared local state (rail name filter + selected
playlist) out of App into a split-context PlaylistsProvider, mirroring
FeedFiltersProvider. Header, PlaylistsRail, and the Playlists detail pane read
it via usePlaylists()/usePlaylistsActions() instead of props drilled through
App; the modules take only a uniform `me` prop now. App loses two useStates and
the selected-playlist persistence helper. (Platform S6b.2)