Channel features: subscribers, new-videos badges, activity-driven sync

- Store subscriber count from YouTube statistics and show it on channel page
- Sync 50 videos per channel with playlistItems pagination support
- Show per-channel and per-category new-videos counters (2-day window)
- Replace hourly videos sync with activity trigger (2h idle) and
  incremental backfill (hard cap 200 per channel)
- Clicking the sidebar new-videos count filters the category feed to
  recent videos only (new_only)
- Update agent-team docs: deploy after green checks

frontend/src/components/AppShell.tsx

@@ -49,7 +49,10 @@ function Sidebar({ close }: { close: () => void }) {
     </div>
     <div className="sidebar-group sidebar-categories">
       <div className="sidebar-heading">Категории</div>
-      {categories.map((category) => <NavLink key={category.id} to={`/category/${category.id}`} onClick={close} className={({ isActive }) => `sidebar-link category-link ${isActive ? 'active' : ''}`}><span className="category-dot" /><span className="truncate">{category.name}</span><span className="sidebar-count">{category.channel_count}</span></NavLink>)}
+      {categories.map((category) => <div key={category.id} className="sidebar-category-row">
+        <NavLink to={`/category/${category.id}`} onClick={close} className={({ isActive }) => `sidebar-link category-link ${isActive ? 'active' : ''}`}><span className="category-dot" /><span className="truncate">{category.name}</span></NavLink>
+        {category.new_videos_count > 0 && <Link to={`/category/${category.id}?new=1`} onClick={close} className="sidebar-badge sidebar-badge-link" aria-label={`${category.new_videos_count} новых видео в категории «${category.name}»`}>{category.new_videos_count}</Link>}
+      </div>)}
       {categories.length === 0 && !categoriesQuery.isLoading && <p className="sidebar-hint">Пока нет категорий</p>}
       <Link to="/settings/categories" onClick={close} className="sidebar-link sidebar-add"><Icon name="plus" size={18} /><span>Новая категория</span></Link>
     </div>