E5 S7: Plex filter UI — listbox-select pickers + studio filter

Reworks the always-expanded filter chip walls into compact, Seerr-style
"+ Add" → searchable-popover pickers (the user's space-saving ask), and adds
the missing studio filter.

- New MultiSelectChips: selected values as removable chips + a "+ Add" trigger
  opening a searchable checklist (AnchoredPopover platform — menuitemcheckbox,
  arrow/Escape, anchor flip). Options carry facet counts; a large vocabulary
  renders a 50-row cap + "N more — refine with search" footer (studios run to
  ~1500). Replaces the flat Genre + Age-rating chip lists.
- New Studio filter via the same picker. Backend: /facets now aggregates the
  studio vocabulary (distinct studio + count, self-excluded like genres). The
  studio filter itself already existed (only addable from the detail page before).
- Collection converted to the same "+ Add" pattern (CollectionPicker): a
  single-select popover with server-side search + the 50-cap; the selected
  collection still shows as a removable chip. Retires the always-inline search+list.

New i18n plex.filter.studio/add/moreRefine + common.search/remove/noResults
(en+hu). Tests: MultiSelectChips.dom.test.tsx (5, incl. the cap) +
test_plex_facets studio-vocabulary. Browser-E2E'd: Genre→Horror(402),
Studio→A24(14, capped/searched), Collection→James Bond(26)/harry-search.
Gate: vitest 342, backend lane 403.

backend/tests/test_plex_facets.py

@@ -12,7 +12,33 @@ import app.state as state
 from app.auth import current_user
 from app.db import get_db
 from app.main import app
-from app.models import PlexLibrary, PlexShow, User
+from app.models import PlexItem, PlexLibrary, PlexShow, User
+
+
+def test_facets_returns_studio_vocabulary(db, monkeypatch):
+    """E5 S7: /facets returns the studio vocabulary (distinct studio + count) for the sidebar picker."""
+    lib = PlexLibrary(plex_key="1", title="Movies", kind="movie", enabled=True)
+    db.add(lib)
+    db.flush()
+    db.add_all([
+        PlexItem(rating_key="m1", library_id=lib.id, kind="movie", title="A", studio="Pixar"),
+        PlexItem(rating_key="m2", library_id=lib.id, kind="movie", title="B", studio="Pixar"),
+        PlexItem(rating_key="m3", library_id=lib.id, kind="movie", title="C", studio="A24"),
+        PlexItem(rating_key="m4", library_id=lib.id, kind="movie", title="D"),  # no studio
+    ])
+    user = User(email="studiofacets@example.com")
+    db.add(user)
+    db.commit()
+    monkeypatch.setattr(state, "_configured_cache", True)
+    app.dependency_overrides[get_db] = lambda: db
+    app.dependency_overrides[current_user] = lambda: user
+    try:
+        resp = TestClient(app).get("/api/plex/facets?scope=movie")
+    finally:
+        app.dependency_overrides.clear()
+    assert resp.status_code == 200, resp.text
+    studios = {s["value"]: s["count"] for s in resp.json()["studios"]}
+    assert studios == {"Pixar": 2, "A24": 1}
 
 
 def test_facets_survives_json_null_genres(db, monkeypatch):