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).

frontend/src/components/ChannelPage.tsx

@@ -81,8 +81,9 @@ export default function ChannelPage({
   const [bannerAttempt, setBannerAttempt] = useState(0);
 
   // A LIVE query: while THIS user's full-history backfill is running, poll so the stored count (and
-  // the N/S/L breakdown) climb on their own — the scheduler adds videos in ~2-min ticks — then stop
-  // polling once the back-catalogue is in. Same queryKey as before, so mutation invalidations still hit.
+  // the N/S/L breakdown) climb on their own — the immediate backfill fills it in seconds, and the
+  // scheduler tops up any tail on its ~10-minute ticks — then stop polling once the back-catalogue is
+  // in. Same queryKey as before, so mutation invalidations still hit.
   const detail = useLiveQuery(qk.channel(channelId), () => api.channelDetail(channelId), {
     intervalMs: (d) => (d?.deep_requested && !d.backfill_done ? 4000 : false),
   });

frontend/src/components/Channels.tsx

@@ -249,10 +249,9 @@ export default function Channels() {
     (c) => !q || `${c.title ?? ""} ${c.handle ?? ""}`.toLowerCase().includes(q),
   );
   // Sync-status pre-filter (top chips → `filters.sync`), applied before the table/cards see the rows.
-  const syncedChannels = useMemo(
-    () => applySyncFilter(visibleChannels, filters.sync),
-    [visibleChannels, filters.sync],
-  );
+  // (Inline, not memoised: `visibleChannels` is a fresh array each render, so a useMemo keyed on it
+  // could never hit its cache — and applySyncFilter is a cheap single pass anyway.)
+  const syncedChannels = applySyncFilter(visibleChannels, filters.sync);
   const s = statusQuery.data;
 
   const onView = (c: ManagedChannel) =>

frontend/src/components/channelColumns.dom.test.tsx

@@ -19,9 +19,6 @@ const ch = (over: Partial<ManagedChannel>): ManagedChannel => ({
   stored_videos: 0,
   last_video_at: null,
   total_duration_seconds: 0,
-  count_normal: 0,
-  count_short: 0,
-  count_live: 0,
   priority: 0,
   hidden: false,
   deep_requested: false,

frontend/src/lib/api/channels.ts

@@ -73,9 +73,6 @@ export interface ManagedChannel {
   stored_videos: number;
   last_video_at: string | null;
   total_duration_seconds: number;
-  count_normal: number;
-  count_short: number;
-  count_live: number;
   priority: number;
   hidden: boolean;
   deep_requested: boolean;