fix(channels): address R14 code-review findings

- list_channels no longer computes the Normal/Shorts/Live aggregation the
  frontend stopped reading when R14 dropped the N/S/L table column; the dead
  ManagedChannel.count_* fields are gone too.
- Immediate "get full history" backfill now coordinates with the paced
  scheduler via a small in-flight set: capped at 2 concurrent + per-channel
  dedup, and run_deep_backfill skips a channel an immediate backfill owns —
  killing the cursor race and bounding the quota-drain burst, without losing
  the speed win.
- Add test_channel_backfill.py: the channelDetail N/S/L counts + the guard's
  no-op / cap / scheduler-skip behaviour.
- Inline the syncedChannels useMemo (its dep is a fresh array each render, so
  it never cached); fix the stale "~2-min ticks" comment (it's 10 minutes).

backend/app/routes/channels.py

@@ -50,20 +50,19 @@ def list_channels(
     ).all()
 
     # Per-channel aggregates over the shared catalog in ONE grouped pass: stored count, last
-    # upload, total duration, and a Normal/Shorts/Live breakdown. Cheap — a single grouped scan
-    # (~35 ms over the full 233k-row catalog on the dev DB), so computed on read rather than
+    # upload, total duration. Cheap — a single grouped scan, so computed on read rather than
     # denormalised (measure-first: reads aren't frequent/hot enough to warrant cached columns).
+    # (The Normal/Shorts/Live breakdown moved to the channel-detail page in R14, so it is no longer
+    # computed here — the manager table dropped its N/S/L column.)
     channel_ids = [c.id for _, c in rows]
     agg: dict[str, dict] = {}
     if channel_ids:
-        for cid, n, last_up, total_dur, shorts, live in db.execute(
+        for cid, n, last_up, total_dur in db.execute(
             select(
                 Video.channel_id,
                 func.count(Video.id),
                 func.max(Video.published_at),
                 func.coalesce(func.sum(Video.duration_seconds), 0),
-                func.count(Video.id).filter(Video.is_short.is_(True)),
-                func.count(Video.id).filter(Video.live_status.in_(LIVE_OR_UPCOMING)),
             )
             .where(Video.channel_id.in_(channel_ids))
             .group_by(Video.channel_id)
@@ -72,9 +71,6 @@ def list_channels(
                 "stored": n,
                 "last_video_at": iso(last_up),
                 "total_duration_seconds": int(total_dur or 0),
-                "count_short": int(shorts),
-                "count_live": int(live),
-                "count_normal": max(0, int(n) - int(shorts) - int(live)),
             }
 
     # Channels already in the *global* deep-backfill queue — i.e. at least one user (any
@@ -108,9 +104,6 @@ def list_channels(
             "stored_videos": (agg.get(ch.id) or {}).get("stored", 0),
             "last_video_at": (agg.get(ch.id) or {}).get("last_video_at"),
             "total_duration_seconds": (agg.get(ch.id) or {}).get("total_duration_seconds", 0),
-            "count_normal": (agg.get(ch.id) or {}).get("count_normal", 0),
-            "count_short": (agg.get(ch.id) or {}).get("count_short", 0),
-            "count_live": (agg.get(ch.id) or {}).get("count_live", 0),
             "priority": sub.priority,
             "hidden": sub.hidden,
             "deep_requested": sub.deep_requested,