refactor: address code-review — layering + public API naming

Applies the three findings from the /code-review high pass on this stack:

1. to_tsquery_str moved from app.feedquery to app.utils — it's a generic
   tsquery sanitizer with no feed dependency; housing it in the feed
   read-model coupled the Plex browse module to the feed domain. Both feed
   and plex now import it from the neutral util module.

2. feedquery.decode_cursor no longer raises fastapi.HTTPException — it raises
   a plain ValueError, and routes/feed.get_feed translates it to the HTTP 400.
   The read-model no longer imports fastapi, matching its "no request state"
   docstring.

3. Dropped the leading underscore on the helpers that are now a cross-module
   public API: feedquery {filtered_query, sort_keys, order_by, keyset_predicate,
   encode_cursor, decode_cursor}; plex.query {TS_CONFIG, FIELD_COLUMNS,
   field_recheck, split_csv, added_cutoff, meta_filter_conds, apply_meta_filters,
   like_escape}; plex.cards {movie_card, show_card, episode_card, leaf_card}.
   Genuinely-internal helpers (_channel_url, _saved_expr, _ADDED_WINDOWS,
   _lib_key) keep their underscore.

Pure code motion + rename. DB-lane suite 287 passed / 2 skipped; ruff clean.

backend/app/routes/feed.py

@@ -11,13 +11,13 @@ from app import quota
 from app.auth import current_user
 from app.db import get_db
 from app.feedquery import (
-    _decode_cursor,
-    _encode_cursor,
-    _filtered_query,
-    _keyset_predicate,
-    _order_by,
-    _sort_keys,
+    decode_cursor,
+    encode_cursor,
+    filtered_query,
+    keyset_predicate,
+    order_by,
     serialize,
+    sort_keys,
 )
 from app.models import (
     ChannelTag,
@@ -91,25 +91,30 @@ def get_feed(
     user: User = Depends(current_user),
     db: Session = Depends(get_db),
 ) -> dict:
-    query, rank_expr = _filtered_query(db, user, **params)
-    keys = _sort_keys(sort, seed, rank_expr)
+    query, rank_expr = filtered_query(db, user, **params)
+    keys = sort_keys(sort, seed, rank_expr)
 
     # Expose each key column on the row so we can build the next cursor from the last item.
     query = query.add_columns(*[k["expr"].label(f"_k{i}") for i, k in enumerate(keys)])
-    query = query.order_by(*_order_by(keys))
+    query = query.order_by(*order_by(keys))
 
     if cursor:
-        vals, cursor_id = _decode_cursor(keys, cursor)
+        # The read-model raises a plain ValueError on a malformed cursor; translate it to the
+        # HTTP 400 here so feedquery stays web-framework-free.
+        try:
+            vals, cursor_id = decode_cursor(keys, cursor)
+        except ValueError:
+            raise HTTPException(status_code=400, detail="Invalid feed cursor")
         for k, v in zip(keys, vals):
             k["value"] = v
-        query = query.where(_keyset_predicate(keys, cursor_id))
+        query = query.where(keyset_predicate(keys, cursor_id))
 
     rows = db.execute(query.limit(limit + 1)).all()
     has_more = len(rows) > limit
     page = rows[:limit]
     return {
         "items": [serialize(r) for r in page],
-        "next_cursor": _encode_cursor(keys, page[-1]) if (has_more and page) else None,
+        "next_cursor": encode_cursor(keys, page[-1]) if (has_more and page) else None,
         "has_more": has_more,
         "limit": limit,
     }
@@ -121,7 +126,7 @@ def get_feed_count(
     user: User = Depends(current_user),
     db: Session = Depends(get_db),
 ) -> dict:
-    query, _rank = _filtered_query(db, user, **params)
+    query, _rank = filtered_query(db, user, **params)
     total = db.scalar(select(func.count()).select_from(query.subquery()))
     return {"count": total or 0}
 
@@ -149,7 +154,7 @@ def get_facets(
         # keeps them applied, so each remaining chip narrows to channels that ALSO have all
         # already-selected topics — and tags that can't co-occur drop to zero (hidden).
         conjunctive = category == "topic" and params.get("tag_mode") == "and"
-        base, _rank = _filtered_query(
+        base, _rank = filtered_query(
             db,
             user,
             **{**params, "exclude_tag_category": None if conjunctive else category},