fix(sort): address R13 S1 review findings

- PlexSidebar activeCount now compares the HEALED sort, so an out-of-scope key
  (movie "duration" after switching to shows) no longer inflates the
  active-filter badge while the control + grid show the default.
- PlexProvider strips the legacy `sortDir` from the filters blob, so it stops
  leaking into the facets query key and being re-persisted on every change.
- PlexProvider sort migration guards the fall-through: valid JSON that isn't a
  SortState now falls back instead of using the raw JSON string as the key.
- New shared healPlexSort(sort, scope) is the single heal both PlexBrowse and
  PlexSidebar use (removes the noop-label plexSortOptions call + the duplication).
- Tests: useSortState.dom.test.ts (hydrate/persist/heal round-trip via renderHook)
  and SortControl.dom.test.tsx (options, pick, direction toggle, directionless,
  trailing). vitest 94 -> 105.

Gate green: tsc/eslint(0 err)/prettier/knip clean, vitest 105.

frontend/src/components/PlexSidebar.tsx

@@ -4,8 +4,7 @@ import { useTranslation } from "react-i18next";
 import { useQuery, useQueryClient } from "@tanstack/react-query";
 import { Layers, ListMusic, Plus, SlidersHorizontal, X } from "lucide-react";
 import { api, EMPTY_PLEX_FILTERS, plexFilterCount, type PlexFilters } from "../lib/api";
-import { healSort } from "../lib/columnSort";
-import { plexSortOptions, PLEX_SORT_FALLBACK } from "../lib/plexSort";
+import { healPlexSort, plexSortOptions, PLEX_SORT_FALLBACK } from "../lib/plexSort";
 import { defaultLayout, type PanelLayout } from "../lib/panelLayout";
 import { useDebounced } from "../lib/useDebounced";
 import { useScrollFade } from "../lib/useScrollFade";
@@ -115,7 +114,10 @@ export default function PlexSidebar({ layout, setLayout, collapsed, onToggleColl
   const collections = collectionsQ.data?.collections ?? [];
 
   const fCount = plexFilterCount(filters);
-  const activeCount = fCount + (show !== "all" ? 1 : 0) + (sort && sort.key !== "title" ? 1 : 0);
+  // Heal against the current scope so a stale out-of-scope key (e.g. movie "duration" after switching
+  // to shows) doesn't inflate the active-filter count while the control + grid show the default.
+  const healedSort = healPlexSort(sort, scope);
+  const activeCount = fCount + (show !== "all" ? 1 : 0) + (healedSort.key !== "title" ? 1 : 0);
   const anyActive = activeCount > 0;
 
   const patch = (p: Partial<PlexFilters>) => setFilters({ ...filters, ...p });
@@ -219,7 +221,7 @@ export default function PlexSidebar({ layout, setLayout, collapsed, onToggleColl
       body: (
         <SortControl
           options={sortOptions}
-          sort={healSort(sort, sortOptions, PLEX_SORT_FALLBACK)}
+          sort={healedSort}
           onChange={(next) => setSort(next ?? PLEX_SORT_FALLBACK)}
           label={t("plex.filter.sort")}
           ascLabel={t("plex.filter.dir.asc")}