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/components/NavSidebar.tsx

@@ -8,6 +8,7 @@ import {
   Bell,
   ChevronLeft,
   ChevronRight,
+  Clapperboard,
   Download,
   Home,
   Info,
@@ -162,6 +163,8 @@ export default function NavSidebar({
     { page: "feed", icon: Home, label: t("header.account.feed") },
     { page: "channels", icon: Tv, label: t("header.account.channels") },
     { page: "playlists", icon: ListVideo, label: t("header.account.playlists") },
+    // Optional Plex module — browse/play your Plex library. Shown only when the admin enabled it.
+    ...(me.plex_enabled ? [{ page: "plex" as Page, icon: Clapperboard, label: t("plex.navLabel") }] : []),
     { page: "notifications", icon: Bell, label: t("inbox.navLabel"), badge: unread },
     // Direct messaging — its own module; hidden for the shared demo account.
     ...(me.is_demo