refactor(plex): move content_libs down into the query layer

The browse scope is a pure DB query with no request state, but it lived in
routes/plex/_shared.py. E24's Home surface needs the same scope from a domain
package, and a domain package importing from routes/ inverts the one-way
dependency CLAUDE.md draws.

Moved to app/plex/query.py and renamed to content_libs (public — it is a domain
helper now). Swept all five call sites and both tests in one go rather than
leaving a re-export shim: the canonical-patterns table already names the
routes.admin re-export as the anti-pattern.

backend/tests/test_plex_overlay.py

@@ -12,7 +12,7 @@ import app.plex.sync as syncmod
 from app import sysconfig
 from app.models import PlexItem, PlexLibrary
 from app.plex.sync import _apply_item, _canonical_guid, _sync_overlay
-from app.routes.plex._shared import _content_libs
+from app.plex.query import content_libs
 
 
 class _StubPlex:
@@ -155,7 +155,7 @@ def test_sync_designates_overlay_and_writes_hu(db, monkeypatch):
     assert m.title_hu == "Öldöklés"
     assert m.genres_hu == ["Akció"]
     # The HU section is not browsable and mirrored no rows of its own.
-    movie_ids, _ = _content_libs(db)
+    movie_ids, _ = content_libs(db)
     assert en.id in movie_ids and hu.id not in movie_ids
     assert db.scalar(select(func.count(PlexItem.id)).where(PlexItem.library_id == hu.id)) == 0
     assert stats["overlaid"] == 1
@@ -240,7 +240,7 @@ def test_content_libs_excludes_overlay_libraries(db):
     db.add(overlay)
     db.commit()
 
-    movie_ids, show_ids = _content_libs(db)
+    movie_ids, show_ids = content_libs(db)
     assert en_lib.id in movie_ids
     assert overlay.id not in movie_ids  # the HU overlay is never browsable
     assert show_ids == [en_shows.id]

backend/tests/test_plex_person.py

@@ -1,6 +1,6 @@
 """DB-backed regression (E5 S4): GET /api/plex/person/{name} returns a cast/crew member's
 filmography — movies + shows in the ENABLED libraries whose cast OR directors include the name,
-each carrying the caller's watch-state, plus the cached headshot. Also covers `_content_libs`
+each carrying the caller's watch-state, plus the cached headshot. Also covers `content_libs`
 scoping (disabled libraries excluded) and the kind filter (episodes are not movies).
 
 Uses the DB lane (`db` fixture) — skipped when no Postgres is reachable.
@@ -20,7 +20,7 @@ from app.models import (
     PlexState,
     User,
 )
-from app.routes.plex._shared import _content_libs
+from app.plex.query import content_libs
 
 NAME = "Robert De Niro"
 
@@ -151,5 +151,5 @@ def test_content_libs_partitions_only_enabled(db):
         ]
     )
     db.commit()
-    movie_ids, show_ids = _content_libs(db)
+    movie_ids, show_ids = content_libs(db)
     assert len(movie_ids) == 1 and len(show_ids) == 1  # the disabled movie lib is excluded