feat(search): ephemeral results, count selector, blocklist, new-first ordering (backend)

- Live-search results stay ephemeral: the discovery-cleanup job now also reclaims un-kept
  via_search videos (no watch state / not playlisted / channel not subscribed) after a grace
  period (search_grace_days), and POST /api/search/clear discards a given result set 'as if
  never added' (drops the user's search-finds + deletes the now-orphaned, un-kept videos).
  Admin POST /api/admin/purge-discovery runs it on demand (grace 0).
- Count selector: GET /api/search/youtube gains a 'limit' — the free scrape source pages
  through continuations until that many results are gathered (no manual load-more); the API
  source stays one ≤50 page (cost).
- Per-user channel blocklist (migration 0034 blocked_channels): block/unblock/list endpoints;
  blocked channels' videos are dropped from live search before ingest and hidden from the feed
  / Library / explore / channel page; explore refuses a blocked channel.
- New-first ordering: results you already have (subscribed channel, watched/in-progress/saved/
  playlisted) sink below genuinely-new discoveries, preserving relevance within each group.

backend/app/sync/explore.py

@@ -143,3 +143,38 @@ def purge_unkept_explored(db: Session) -> dict:
         "videos_deleted": videos_deleted,
         "channels_deleted": channels_deleted,
     }
+
+
+def purge_unkept_search(db: Session, grace_days: int | None = None) -> dict:
+    """Remove live-search result videos nobody kept, after a grace period — "as if never added".
+
+    A `via_search` video is KEPT (and spared) when anyone has watched / in-progress / hidden it
+    (a VideoState), saved/playlisted it (a PlaylistItem), or subscribes to its channel (it's then
+    organically owned). A bare SearchFind does NOT count — it's the ephemeral "shown in search"
+    marker itself — so a result you only glanced at is reclaimed. Deleting the video cascades its
+    SearchFinds. `grace_days=0` purges immediately (the admin "purge now" path); None uses config.
+    0 quota."""
+    grace = sysconfig.get_int(db, "search_grace_days") if grace_days is None else grace_days
+    cutoff = _now() - timedelta(days=grace)
+    state_exists = select(VideoState.id).where(VideoState.video_id == Video.id).exists()
+    pl_exists = select(PlaylistItem.id).where(PlaylistItem.video_id == Video.id).exists()
+    sub_exists = (
+        select(Subscription.id).where(Subscription.channel_id == Video.channel_id).exists()
+    )
+    deleted = db.execute(
+        delete(Video).where(
+            Video.via_search.is_(True),
+            Video.created_at < cutoff,
+            ~state_exists,
+            ~pl_exists,
+            ~sub_exists,
+        )
+    ).rowcount
+    db.commit()
+    return {"search_videos_deleted": deleted}
+
+
+def purge_ephemeral(db: Session) -> dict:
+    """The scheduler's discovery-cleanup pass: reclaim un-kept explored channels AND un-kept
+    live-search result videos in one run."""
+    return {**purge_unkept_explored(db), **purge_unkept_search(db)}