feat(plex): P1.5 — Plex as a nav module + integrated search + filter sidebar

Per user feedback: promote Plex from a hidden feed-Source option to a first-class
left-nav module, with its own filter sidebar and the shared top search box.

- Plex is now a nav-rail module (page='plex', gated on me.plex_enabled) — its own
  page → correct browser Back/Forward; removed the Feed Source-dropdown 'plex' hack.
- PlexSidebar.tsx: left filter column (library scope, watch-state for movies:
  all/unwatched/in_progress/watched, sort) — per-account persisted (App state).
- Header search box now also serves the Plex page (integrated search); the live
  YouTube-search escalation stays feed-only.
- PlexBrowse.tsx reworked: infinite scroll (IntersectionObserver, no 'Load more'),
  content-visibility for smoother long-list scroll, show drill-down rides history
  (useHistorySubview) so Back returns to the grid; dropped the stray 'YouTube feed'
  button on the show page.
- backend /browse gains a per-user watch-state filter (show=, movies only).
- plex i18n (navLabel + filter.*) en/hu/de.

Note: episode-title 'Episode N' on some shows (e.g. Westworld) is Plex-side
(unmatched show) — we mirror what Plex has; Match/Refresh in Plex + re-sync fixes it.

frontend/src/App.tsx

@@ -63,6 +63,7 @@ import { CURRENT_VERSION } from "./lib/releaseNotes";
 // never reach non-admins. All are rendered inside a <Suspense> boundary below.
 const Feed = lazy(() => import("./components/Feed"));
 const PlexBrowse = lazy(() => import("./components/PlexBrowse"));
+const PlexSidebar = lazy(() => import("./components/PlexSidebar"));
 const ChannelPage = lazy(() => import("./components/ChannelPage"));
 const Channels = lazy(() => import("./components/Channels"));
 const Playlists = lazy(() => import("./components/Playlists"));
@@ -242,6 +243,10 @@ export default function App() {
   const [channelsViewRaw, setChannelsView] = useAccountPersistedState(LS.channelsView, "subscribed");
   const channelsView: ChannelsView =
     channelsViewRaw === "discovery" ? "discovery" : "subscribed";
+  // Plex module filters (its own left-sidebar filter section) — per-account persisted.
+  const [plexLib, setPlexLib] = useAccountPersistedState(LS.plexLibrary, "");
+  const [plexShowFilter, setPlexShowFilter] = useAccountPersistedState(LS.plexShow, "all");
+  const [plexSort, setPlexSort] = useAccountPersistedState(LS.plexSort, "added");
   // Bumped to tell the channel manager to drop a stale column filter when we send the user
   // there to see a specific set (the header's "without full history" link).
   const [channelsFilterReset, setChannelsFilterReset] = useState(0);
@@ -713,6 +718,20 @@ export default function App() {
           onToggleCollapse={() => setFilterCollapsed(!filterCollapsed)}
         />
       )}
+      {page === "plex" && meQuery.data!.plex_enabled && (
+        <Suspense fallback={null}>
+          <PlexSidebar
+            library={plexLib}
+            setLibrary={setPlexLib}
+            show={plexShowFilter}
+            setShow={setPlexShowFilter}
+            sort={plexSort}
+            setSort={setPlexSort}
+            collapsed={filterCollapsed}
+            onToggleCollapse={() => setFilterCollapsed(!filterCollapsed)}
+          />
+        </Suspense>
+      )}
       <div className="relative flex-1 min-w-0 flex flex-col">
         {channelView ? (
           <Suspense fallback={pageFallback}>
@@ -782,8 +801,8 @@ export default function App() {
               prefs={prefsCtl}
               onOpenWizard={() => setWizardOpen(true)}
             />
-          ) : meQuery.data!.plex_enabled && filters.librarySource === "plex" ? (
-            <PlexBrowse filters={filters} setFilters={setFilters} />
+          ) : page === "plex" && meQuery.data!.plex_enabled ? (
+            <PlexBrowse q={filters.q} library={plexLib} show={plexShowFilter} sort={plexSort} />
           ) : (
             <Feed
               filters={filters}
@@ -791,7 +810,6 @@ export default function App() {
               view={view}
               canRead={meQuery.data!.can_read}
               isDemo={meQuery.data!.is_demo}
-              plexEnabled={meQuery.data!.plex_enabled}
               onOpenWizard={() => setWizardOpen(true)}
               ytSearch={ytSearch}
               onYtSearch={enterYtSearch}