refactor(plex): split browse.py god-module into per-concern routers (E3 S1)

routes/plex/browse.py was a 1693-line god-module (libraries + facets +
collections + playlists + show/item detail + people). Split it into focused
sibling routers under the same /api/plex prefix — pure code motion, no SQL /
route-path / response-shape changes:

  browse.py  1693 -> 469  (list_libraries, unified_library, facets)
  collections.py  (new 253)  browse + admin collection editor; owns _collection_source
  playlists.py    (new 405)  the user's orderable playlists
  detail.py       (new 438)  show/item detail + enrichment; _lib_key lives here
  people.py       (new 139)  cast/crew chips + person filmography

Cross-module helpers _norm_lang + _content_libs move to _shared.py (their one
home); detail imports _collection_source from collections (one-way, no cycle).
__init__.py includes the four new routers. Three DB-lane tests follow the moved
symbols (import path for _content_libs; monkeypatch targets for PlexClient /
_show_enrichment now on detail).

Behaviour-equivalent: ruff clean, 348 DB-lane pass (unchanged), parity net green.

backend/app/routes/plex/__init__.py

@@ -10,9 +10,21 @@ wiring expects (`plex_routes.router`), so main.py is unchanged.
 
 from fastapi import APIRouter
 
-from app.routes.plex import admin, browse, playback
+from app.routes.plex import (
+    admin,
+    browse,
+    collections,
+    detail,
+    people,
+    playback,
+    playlists,
+)
 
 router = APIRouter()
 router.include_router(admin.router)
 router.include_router(browse.router)
+router.include_router(collections.router)
+router.include_router(detail.router)
+router.include_router(people.router)
 router.include_router(playback.router)
+router.include_router(playlists.router)