feat(plex): shareable Plex-browse state in the URL — scope+filters+sort+show (S4)

Mirror the Plex-browse content state into the address bar so a browse view is
bookmarkable/shareable, the Plex analogue of the feed's urlState. Keys are
NAMESPACED (pscope/psort/pshow/pf) rather than reusing the feed's bare
scope/sort/show: FeedFiltersProvider actively strips its own KEYS from the URL
whenever off the feed page, so a shared key would be deleted out from under the
Plex page. The namespaced keys are Plex-unique (like ?v=/?pl), so no other
provider ever reads or clears them.

- New lib/plexUrlState.ts: plexParamUpdates / plexParamsToState / hasPlexParams.
  The pf filter blob reuses the SAME appendPlexFilters wire serializer (new
  public plexFiltersToParams + inverse parsePlexFilters, kept next to each other
  so a new wire key can't be added on one side only).
- PlexProvider: URL-seed wins over localStorage at mount; the account-pin
  rehydrate persists the seed instead of clobbering it (mirrors feed's
  initialHadUrlFilters); useUrlMirror mirrors/clears the 4 keys, gated on
  page===plex. q/field stay out of the shareable contract.
- NavigationProvider: a page switch now also nulls the 4 plex keys.

Tests: 8 new round-trip cases in plexUrlState.dom.test.ts (FE vitest 483→491).

frontend/src/lib/api/plex.ts

@@ -334,6 +334,48 @@ function appendPlexFilters(u: URLSearchParams, f: PlexFilters): void {
   if (f.collections?.length) u.set("collections", f.collections.join(","));
   if (f.collectionMode === "all") u.set("collection_mode", "all");
 }
+
+// Public wrapper over the private appendPlexFilters so the URL mirror (plexUrlState) serializes the
+// filter set through the SAME single source the API request uses — the two can never drift. Display-only
+// titles (collectionTitles) stay out, exactly like the wire params and the saved-view signature.
+export function plexFiltersToParams(f: PlexFilters): URLSearchParams {
+  const u = new URLSearchParams();
+  appendPlexFilters(u, f);
+  return u;
+}
+
+// The inverse of appendPlexFilters: parse a filter sub-querystring back into a full PlexFilters (missing
+// keys → EMPTY defaults). Kept next to its encoder so a new wire key can't be added on one side only.
+export function parsePlexFilters(p: URLSearchParams): PlexFilters {
+  const csv = (k: string): string[] => {
+    const v = p.get(k);
+    return v ? v.split(",").filter(Boolean) : [];
+  };
+  const num = (k: string): number | undefined => {
+    if (!p.has(k)) return undefined;
+    const n = Number(p.get(k));
+    return Number.isFinite(n) ? n : undefined;
+  };
+  const f: PlexFilters = { ...EMPTY_PLEX_FILTERS };
+  f.genres = csv("genres");
+  if (p.get("genre_mode") === "all") f.genreMode = "all";
+  f.contentRatings = csv("content_ratings");
+  f.yearMin = num("year_min");
+  f.yearMax = num("year_max");
+  f.ratingMin = num("rating_min");
+  f.durationMin = num("duration_min");
+  f.durationMax = num("duration_max");
+  const aw = p.get("added_within");
+  if (aw) f.addedWithin = aw;
+  f.directors = csv("directors");
+  f.actors = csv("actors");
+  if (p.get("actor_mode") === "all") f.actorMode = "all";
+  f.studios = csv("studios");
+  f.keywords = csv("keywords");
+  f.collections = csv("collections");
+  if (p.get("collection_mode") === "all") f.collectionMode = "all";
+  return f;
+}
 export interface PlexFacets {
   genres: { value: string; count: number }[];
   content_ratings: { value: string; count: number }[];