fix(search): every related and live-search request takes a slot, and a failed one gives it back

A related list's cursor cost nothing, and a cursor is a free string: a replayed one read and
enriched without end. Every request now takes a slot of the user's daily cap — taken under a lock
before the work (`quota.claim_action`), so requests sent together cannot all pass the last free
one, and given back when the request fails outright (`quota.refund_action`). The live search's
scrape source takes its slots the same way.

A limit of 0 turns the feature off: a distinct 409 `related_disabled` / `search_disabled`, and
`/api/me` says `related_enabled` / `search_enabled` so the UI can leave it out.

A videos.list that fails no longer reads as an empty page: `ingest_candidates` raises, and the
search and the related list answer the refusal (the shared budget spent says "quota") instead of
"no results". The two routes' page loops are one (`_gather`).

`clear` deletes only what the caller found: a related list's rows carry no find, and any user
could name them.

backend/app/catalog/search.py

@@ -75,7 +75,8 @@ def ingest_candidates(
 ) -> list[str]:
     """Materialise one page of search candidates into the catalog (channel stubs + enrich,
     video stubs flagged via_search, enrich, Shorts classification) and return the KEEPABLE
-    video ids — non-Short, non-live — in the input relevance order."""
+    video ids — non-Short, non-live — in the input relevance order. A videos.list that fails
+    raises its YouTubeError: with nothing enriched, nothing could be kept."""
     ids = [it["id"] for it in candidates]
     if not ids:
         return []
@@ -132,13 +133,16 @@ def ingest_candidates(
         with quota.attribute(user.id, quota.QuotaAction.VIDEOS_ENRICH):
             detail_by_id = {it["id"]: it for it in yt.get_videos(ids)}
     except YouTubeError:
-        # Every candidate then stays unenriched, and an unenriched video cannot be judged live or
-        # Short — so it is dropped. A working search returns nothing and reads as "no results".
+        # An unenriched video cannot be judged live or Short, so none of this page could be kept:
+        # swallowed, the failure answered as a page with nothing on it — "no results" for a search
+        # that never ran (the shared budget spent, no API key). The stubs stay (`insert_stubs`
+        # committed them), as the channels' do above; the caller answers the failure (its refusal
+        # says which).
         log.warning(
             "the videos found by a search could not be enriched",
             extra=logs.event("search.video_enrich_failed", candidates=len(ids)),
         )
-        detail_by_id = {}
+        raise
     enriched_at = datetime.now(
         timezone.utc
     )  # when THIS enrich ran (distinct from the stub placeholder)
@@ -212,17 +216,25 @@ def clear(db: Session, user: User, video_ids: list[str]) -> int:
     """Discard these results "as if never added": drop this user's finds of them, then delete the
     ones nobody kept — a `via_search` video no reader holds (`reader.queries.kept_by_a_reader`),
     whose channel nobody subscribes to, and that no other user still has as a find. Returns how
-    many videos went."""
-    db.execute(
-        delete(SearchFind).where(
-            owned_by(SearchFind.user_id, user), SearchFind.video_id.in_(video_ids)
+    many videos went.
+
+    Only the ones this user found: a video in the catalog with no find at all (a related list's,
+    which records none) is in someone's list right now, and an id any user could name would let
+    them delete it from under that list."""
+    mine = list(
+        db.scalars(
+            delete(SearchFind)
+            .where(owned_by(SearchFind.user_id, user), SearchFind.video_id.in_(video_ids))
+            .returning(SearchFind.video_id)
         )
     )
+    if not mine:
+        return 0
     subscribed = select(Subscription.id).where(Subscription.channel_id == Video.channel_id).exists()
     other_find = select(SearchFind.id).where(SearchFind.video_id == Video.id).exists()
     result = db.execute(
         delete(Video).where(
-            Video.id.in_(video_ids),
+            Video.id.in_(mine),
             Video.via_search.is_(True),
             ~reader_queries.kept_by_a_reader(Video.id),
             ~subscribed,