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/PlexProvider.tsx

@@ -72,12 +72,17 @@ export function PlexProvider({ children }: { children: ReactNode }) {
   const [sort, setSortState] = useState<SortState>(() => {
     const raw = getAccountRaw(LS.plexSort);
     if (!raw) return PLEX_SORT_FALLBACK;
+    let wasJson = false;
     try {
       const parsed = parseSortState(JSON.parse(raw));
+      wasJson = true;
       if (parsed) return parsed;
     } catch {
-      /* legacy bare-key string handled below */
+      /* not JSON → a legacy bare-key string, handled below */
     }
+    // Valid JSON that wasn't a SortState is corrupt — fall back rather than treat the JSON text as a
+    // key. Only a non-JSON raw is a genuine legacy bare key.
+    if (wasJson) return PLEX_SORT_FALLBACK;
     let dir: "asc" | "desc" = "asc";
     try {
       if (
@@ -94,7 +99,10 @@ export function PlexProvider({ children }: { children: ReactNode }) {
   const [filtersRaw, setFiltersRaw] = useState<string>(() => getAccountRaw(LS.plexFilters) ?? "{}");
   const filters = useMemo<PlexFilters>(() => {
     try {
-      return { ...EMPTY_PLEX_FILTERS, ...JSON.parse(filtersRaw) };
+      // Drop the legacy `sortDir` — direction now lives in the sort SortState. Left here it would leak
+      // into the facets query key and be re-persisted on every filter change.
+      const { sortDir: _drop, ...rest } = JSON.parse(filtersRaw);
+      return { ...EMPTY_PLEX_FILTERS, ...rest };
     } catch {
       return EMPTY_PLEX_FILTERS;
     }