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/i18n/locales/en/plex.json

@@ -1,4 +1,5 @@
 {
+  "navLabel": "Plex",
   "backToFeed": "YouTube feed",
   "backToLibrary": "Back to library",
   "searchPlaceholder": "Search Plex…",
@@ -6,8 +7,20 @@
     "added": "Recently added",
     "title": "Title"
   },
+  "filter": {
+    "library": "Library",
+    "show": "Show",
+    "showOpt": {
+      "all": "All",
+      "unwatched": "Unwatched",
+      "in_progress": "In progress",
+      "watched": "Watched"
+    },
+    "sort": "Sort"
+  },
   "count": "{{count}} titles",
   "searchCount": "{{count}} matches",
+  "noMatches": "No matches.",
   "loading": "Loading…",
   "empty": "Nothing here yet. Run a Plex sync from the admin Config page.",
   "loadMore": "Load more",