fix(channels): address R14 deep-review findings

- Make the immediate-backfill guard SYMMETRIC: run_deep_backfill now also
  registers the channel it pages in _backfill_in_progress, so it and
  backfill_channel_now mutually exclude per-channel and never advance the
  same cursor concurrently (whichever started first). The interactive cap
  moves to a separate _immediate_running counter so the scheduler's channels
  don't false-trip it.
- Attribute the immediate backfill's spend: wrap it in
  quota.attribute(user_id, VIDEOS_BACKFILL_FULL) (route passes user.id), so
  it shows under the user's full-backfill action, not the OTHER/system bucket.
- Tests: the update_channel->background-task wiring + the demo guard
  (scheduled for a real user, NOT for demo); distinct N/S/L counts (2 short
  + 1 live) so a short/live swap fails; extracted channelDetailPollMs with a
  pure unit test of the poll-or-stop predicate.
- a11y: role="img" on the fully-synced charm so screen readers announce it.

frontend/src/components/ChannelPage.tsx

@@ -2,6 +2,7 @@ import { useCallback, useEffect, useRef, useState } from "react";
 import { useTranslation } from "react-i18next";
 import { useMutation, useQuery, useQueryClient } from "@tanstack/react-query";
 import { useLiveQuery } from "../lib/useLiveQuery";
+import { channelDetailPollMs } from "../lib/channelDetailPoll";
 import { qk } from "../lib/queryKeys";
 import { useNavigationActions } from "./NavigationProvider";
 import { PriorityStepper } from "./PriorityStepper";
@@ -85,7 +86,7 @@ export default function ChannelPage({
   // 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),
+    intervalMs: channelDetailPollMs,
   });
   const ch = detail.data;
   useEffect(() => setBannerAttempt(0), [ch?.banner_url]); // fresh channel/banner → try again

frontend/src/components/channelColumns.tsx

@@ -52,6 +52,7 @@ function StoredCell({ c }: { c: ManagedChannel }) {
       {isFullySynced(c) && (
         <Tooltip hint={t("channels.row.fullySyncedHint")}>
           <Check
+            role="img"
             className="w-3.5 h-3.5 text-accent shrink-0 cursor-help"
             aria-label={t("channels.row.fullySynced")}
           />

frontend/src/lib/channelDetailPoll.test.ts

@@ -0,0 +1,24 @@
+import { describe, it, expect } from "vitest";
+import { channelDetailPollMs } from "./channelDetailPoll";
+import { type ChannelDetail } from "./api";
+
+// Only deep_requested + backfill_done drive the decision; cast a partial for the pure predicate.
+const d = (over: Partial<ChannelDetail>): ChannelDetail => over as ChannelDetail;
+
+describe("channelDetailPollMs", () => {
+  it("polls at 4s while THIS user's full-history backfill is running", () => {
+    expect(channelDetailPollMs(d({ deep_requested: true, backfill_done: false }))).toBe(4000);
+  });
+
+  it("stops (false) once the back-catalogue is fully in", () => {
+    expect(channelDetailPollMs(d({ deep_requested: true, backfill_done: true }))).toBe(false);
+  });
+
+  it("stops (false) when the user hasn't requested full history", () => {
+    expect(channelDetailPollMs(d({ deep_requested: false, backfill_done: false }))).toBe(false);
+  });
+
+  it("stops (false) before the detail has loaded", () => {
+    expect(channelDetailPollMs(undefined)).toBe(false);
+  });
+});

frontend/src/lib/channelDetailPoll.ts

@@ -0,0 +1,8 @@
+import { type ChannelDetail } from "./api";
+
+/** How often the channel page re-polls its detail (via useLiveQuery): every 4s while THIS user's
+ *  full-history backfill is running (`deep_requested && !backfill_done`) so the stored count + the
+ *  N/S/L breakdown climb on their own, and `false` (stop polling) once the back-catalogue is in or
+ *  the user never requested it. Extracted so the poll-or-stop decision is unit-testable. */
+export const channelDetailPollMs = (d: ChannelDetail | undefined): number | false =>
+  d?.deep_requested && !d.backfill_done ? 4000 : false;