feat(plex): unify movies + shows into one cross-library browser

Collapse the separate Movie/Show library sections into ONE unified library with a
shared search + shared filter sidebar and a Movies/Shows/Both scope selector.

Backend: new GET /api/plex/library — a cross-library UNION of movies (plex_items) and
shows (plex_shows) as one mixed, paginated, sorted feed, scoped movie|show|both, with
the shared filters (extracted into _apply_meta_filters, DRY), FTS search, and per-user
watch-state (a show's state = the aggregate of its episodes). On a search that also
matches episodes, matching episodes come back in a separate 'episodes' list (the grouped
'Episodes' section — Proposal 3). /facets is now scope-aware (merged across the scope's
libraries). /item and /show now return their library section key (for the admin
collection editor, since there's no single library prop in the unified view).

Frontend: PlexSidebar's library picker -> a scope selector (Both/Movies/Shows); facets +
browse follow the scope (App's plexLib repurposed to a validated scope, default both).
PlexBrowse uses the unified endpoint, renders a mixed Titles grid + an Episodes section
on search. Poster cards are generalized: a hover Play/Resume overlay on every card, a
clickable title (not just the poster), and a movie/show type tag. The quick watched
toggle is now optimistic so it reliably flips BOTH ways (fixes the movie card that could
mark but not un-mark). Cast/crew members and the show hero's meta (year/rating/genre/
content-rating) are clickable filters; clicking a person widens the scope to Both so the
result is a mixed movie+show feed. i18n plex.filter.scope*/plex.unified.* (en/hu/de).

Still pending from the polish list (next pass): season-card quick toggles (watched +
add-to-playlist), per-episode watched toggle, and the full glassy art-bg + hide-cast
customize menu on the series pages.

frontend/src/components/PlexInfo.tsx

@@ -143,7 +143,7 @@ export default function PlexInfo({
   const setState = async (status: "new" | "watched") => {
     await api.plexSetState(detail.id, status).catch(() => {});
     qc.invalidateQueries({ queryKey: ["plex-item", detail.id] });
-    qc.invalidateQueries({ queryKey: ["plex-browse"] });
+    qc.invalidateQueries({ queryKey: ["plex-library"] });
     qc.invalidateQueries({ queryKey: ["plex-show"] });
     onStateChange?.();
   };