feat(plex): S6 frontend — language threading, rating badge, i18n parity

E5 S6 frontend half.

Language threading (?lang=hu serves the HU overlay; en is the default):
- api/plex.ts: `lang` on plexLibrary / plexFacets / plexItem / plexShow (only
  sent for hu, so EN URLs stay byte-stable); PlexItemDetail gains `rating`.
- queryKeys: plexItem / plexShow take an optional trailing lang so a switch caches
  HU/EN separately; the ...rest keys (library/facets) already carry it. Prefix
  invalidations (qk.plexShow(id) / qk.plexItem(id)) still match either.
- i18n: plexLang() collapses the UI language to en|hu for non-component code.
- PlexBrowse / PlexSidebar: thread lang into the grid, facets, item and show
  queries (useTranslation re-renders on switch → the key changes → refetch).
- plexPlayerHooks: the optimistic resume setQueryData now keys by plexLang() so
  it still lands on the language-keyed detail query.
- Clear the genre-filter selection on a language switch — genre chips are
  language-specific strings, so a stale one silently empties the grid.

IMDb-only rating badge (folded-in S5b review #5):
- PlexInfo.tsx shows the IMDb badge + imdb.com link only when imdb_rating is
  present; otherwise it renders the Plex audience `rating` (no IMDb link/branding),
  so a non-IMDb score is never mislabelled. ratingMin filter keys off whichever
  score is shown.

Tests: i18n parity.test.ts (en/hu key sets identical per namespace — currently
green, no drift). FE gate green: tsc / knip / lint clean, 213 vitest tests pass.

frontend/src/i18n/index.ts

@@ -56,4 +56,11 @@ export function setLanguage(code: LangCode): void {
   document.documentElement.lang = code;
 }
 
+// The Plex overlay serves only EN or HU metadata (E5 S6). Collapse the active UI language to one of
+// those for the `?lang=` param / query keys. Components read `i18n.language` off useTranslation (which
+// re-renders on switch); this singleton reader is for non-component code (e.g. plexPlayerHooks).
+export function plexLang(): "en" | "hu" {
+  return i18n.language?.startsWith("hu") ? "hu" : "en";
+}
+
 export default i18n;

frontend/src/i18n/parity.test.ts

@@ -0,0 +1,52 @@
+// E5 S6: every locale namespace must carry the SAME key set in English and Hungarian. A key present
+// in one language but not the other renders the raw key string (missing translation) or is dead
+// weight (orphaned translation); this test fails loudly on either, per namespace.
+import { describe, expect, it } from "vitest";
+
+const mods = import.meta.glob("./locales/*/*.json", { eager: true }) as Record<
+  string,
+  { default: Record<string, unknown> }
+>;
+
+function flatten(obj: Record<string, unknown>, prefix = ""): string[] {
+  const out: string[] = [];
+  for (const [k, v] of Object.entries(obj)) {
+    const key = prefix ? `${prefix}.${k}` : k;
+    if (v && typeof v === "object" && !Array.isArray(v)) {
+      out.push(...flatten(v as Record<string, unknown>, key));
+    } else {
+      out.push(key);
+    }
+  }
+  return out.sort();
+}
+
+// { namespace: { en: {...}, hu: {...} } }
+const byNs: Record<string, Record<string, Record<string, unknown>>> = {};
+for (const [path, mod] of Object.entries(mods)) {
+  const m = path.match(/\/locales\/([^/]+)\/([^/]+)\.json$/);
+  const lang = m?.[1];
+  const ns = m?.[2];
+  if (!lang || !ns) continue;
+  (byNs[ns] ??= {})[lang] = mod.default;
+}
+
+describe("i18n en/hu key parity", () => {
+  it("loaded both languages for every namespace", () => {
+    expect(Object.keys(byNs).length).toBeGreaterThan(0);
+    for (const [ns, langs] of Object.entries(byNs)) {
+      expect({ ns, langs: Object.keys(langs).sort() }).toEqual({ ns, langs: ["en", "hu"] });
+    }
+  });
+
+  for (const [ns, langs] of Object.entries(byNs)) {
+    it(`${ns}: en and hu declare identical keys`, () => {
+      const en = flatten(langs.en ?? {});
+      const hu = flatten(langs.hu ?? {});
+      expect({
+        missingInHu: en.filter((k) => !hu.includes(k)),
+        missingInEn: hu.filter((k) => !en.includes(k)),
+      }).toEqual({ missingInHu: [], missingInEn: [] });
+    });
+  }
+});