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/app/plex/query.py

@@ -8,8 +8,9 @@ from datetime import datetime, timedelta, timezone
 
 from sqlalchemy import and_, case, func, or_, select, type_coerce
 from sqlalchemy.dialects.postgresql import JSONB
+from sqlalchemy.orm import Session
 
-from app.models import PlexItem
+from app.models import PlexItem, PlexLibrary
 
 TS_CONFIG = "public.unaccent_simple"
 
@@ -342,3 +343,26 @@ def apply_show_state_filter(query, tot, wat, inp, show: str):
     if show == "unwatched":
         return query.where(wat == 0, inp == 0)
     return query
+
+
+def content_libs(db: Session) -> tuple[list[int], list[int]]:
+    """The BROWSABLE content libraries, partitioned into (movie_lib_ids, show_lib_ids) — the single
+    source of the browse scope. Excludes HU overlay libraries (`overlay_of` set): those are never
+    browsed on their own, they only lend their Hungarian metadata to the EN twin's rows (E5 S5).
+
+    Lives here, in the query layer, rather than in `routes/plex/_shared.py` where it started: E24's
+    Home surface needs the same scope, and a domain package importing from `routes/` would invert the
+    one-way dependency CLAUDE.md draws. It never touched request state, so nothing was lost by the
+    move."""
+    libs = (
+        db.execute(
+            select(PlexLibrary).where(
+                PlexLibrary.enabled.is_(True), PlexLibrary.overlay_of.is_(None)
+            )
+        )
+        .scalars()
+        .all()
+    )
+    movie_lib_ids = [lb.id for lb in libs if lb.kind == "movie"]
+    show_lib_ids = [lb.id for lb in libs if lb.kind == "show"]
+    return movie_lib_ids, show_lib_ids