feat(plex): P1 frontend — Plex feed source, browse/search, show drill-down

- PlexBrowse.tsx: self-contained Plex mode (library scope tabs, own search +
  sort, poster-card grid with watch state + playability tint, paged; show →
  seasons/episodes drill-down). Playback announces (P2 wires the real player).
- Feed source dropdown gains a 'Plex' option (gated on me.plex_enabled); App
  swaps <Feed> for <PlexBrowse> when librarySource==='plex' so the video-feed
  hooks don't run in Plex mode. me exposes plex_enabled.
- api client (plexLibraries/plexBrowse/plexShow/plexImageUrl) + types; librarySource
  union + share-URL restore gain 'plex'; new plex i18n namespace en/hu/de.
- Verified over HTTP (authed): libraries, browse+FTS, image proxy 200 image/jpeg.

frontend/src/lib/api.ts

@@ -13,6 +13,7 @@ export interface Me {
   has_google: boolean;
   has_password: boolean;
   google_enabled: boolean;
+  plex_enabled: boolean;
   can_read: boolean;
   can_write: boolean;
   pending_invites: number;
@@ -179,7 +180,7 @@ export interface FeedFilters {
   show: string;
   // Library (scope "all") only — provenance filter: "organic" (default) hides search-
   // discovered videos, "all" mixes them in, "search" shows only them. Ignored for "my".
-  librarySource?: "organic" | "all" | "search";
+  librarySource?: "organic" | "all" | "search" | "plex";
   channelId?: string;
   channelName?: string;
   maxAgeDays?: number;
@@ -623,6 +624,54 @@ export interface PlexTestResult {
   sections: PlexSection[];
 }
 
+// Plex browse/search/drill-down (the mirrored catalog rendered as feed-style cards).
+export interface PlexLibrary {
+  key: string;
+  title: string;
+  kind: "movie" | "show";
+  count: number;
+}
+export interface PlexCard {
+  id: string;
+  type: "movie" | "show" | "episode";
+  title: string;
+  year?: number | null;
+  duration_seconds?: number | null;
+  thumb: string;
+  playable?: string; // direct | remux | transcode
+  status?: string; // new | watched | hidden
+  position_seconds?: number;
+  season_count?: number | null; // show
+  season_number?: number | null; // episode
+  episode_number?: number | null; // episode
+  summary?: string | null; // episode
+}
+export interface PlexBrowseResult {
+  kind: "movie" | "show";
+  total: number;
+  offset: number;
+  limit: number;
+  items: PlexCard[];
+}
+export interface PlexSeasonDetail {
+  id: string;
+  season_number: number | null;
+  title: string;
+  thumb: string;
+  episodes: PlexCard[];
+}
+export interface PlexShowDetail {
+  show: {
+    id: string;
+    title: string;
+    summary?: string | null;
+    year?: number | null;
+    thumb: string;
+    art: string;
+  };
+  seasons: PlexSeasonDetail[];
+}
+
 // Admin Users & roles page.
 export interface AdminUserRow {
   id: number;
@@ -936,6 +985,27 @@ export const api = {
   testEmail: (): Promise<{ sent: boolean; to: string }> =>
     req("/api/admin/config/test-email", { method: "POST" }),
   testPlex: (): Promise<PlexTestResult> => req("/api/plex/test", { method: "POST" }),
+  syncPlex: (): Promise<Record<string, unknown>> => req("/api/plex/sync", { method: "POST" }),
+  plexLibraries: (): Promise<{ enabled: boolean; libraries: PlexLibrary[] }> =>
+    req("/api/plex/libraries"),
+  plexBrowse: (p: {
+    library: string;
+    q?: string;
+    sort?: string;
+    offset?: number;
+    limit?: number;
+  }): Promise<PlexBrowseResult> => {
+    const u = new URLSearchParams({ library: p.library });
+    if (p.q) u.set("q", p.q);
+    if (p.sort) u.set("sort", p.sort);
+    if (p.offset) u.set("offset", String(p.offset));
+    if (p.limit) u.set("limit", String(p.limit));
+    return req(`/api/plex/browse?${u.toString()}`);
+  },
+  plexShow: (id: string): Promise<PlexShowDetail> =>
+    req(`/api/plex/show/${encodeURIComponent(id)}`),
+  plexImageUrl: (id: string, variant?: "thumb" | "art"): string =>
+    `/api/plex/image/${encodeURIComponent(id)}${variant === "art" ? "?variant=art" : ""}`,
   // --- admin: users & roles ---
   adminUsers: (): Promise<AdminUserRow[]> => req("/api/admin/users"),
   setUserRole: (id: number, role: "user" | "admin"): Promise<AdminUserRow> =>