feat: sync status indicator, admin pause/resume, filtered video count

- Header shows a live sync status (total videos + channels still backfilling, or
  "paused"), polled every 30s
- Admins can pause/resume the background sync; a paused flag in app_state makes
  scheduled jobs skip (migration 0006)
- GET /api/feed/count returns the number of videos matching the current filters;
  shared filter builder keeps it in sync with /api/feed; shown above the feed
- /api/sync/status reports backfill progress, pending enrichment and paused state

frontend/src/components/Header.tsx

@@ -10,6 +10,7 @@ import {
 } from "lucide-react";
 import { SCHEMES, type Scheme, type ThemePrefs } from "../lib/theme";
 import type { FeedFilters, Me } from "../lib/api";
+import SyncStatus from "./SyncStatus";
 
 function IconBtn(props: React.ButtonHTMLAttributes<HTMLButtonElement>) {
   const { className = "", ...rest } = props;
@@ -91,6 +92,8 @@ export default function Header({
         Sub<span className="text-accent">feed</span>
       </div>
 
+      <SyncStatus />
+
       <div className="flex-1 max-w-xl mx-auto relative">
         <Search className="w-4 h-4 absolute left-3 top-1/2 -translate-y-1/2 text-muted" />
         <input