feat(apes-sidebar): Phase 2 — badge 计数 + auto-collapse（visible 门控暂停）

- apes:tasks badge = running 会话数；apes:agents badge = subagent 数
  （纯 (ctx)=>number|null 函数，0→null 隐藏，host 封顶 99+）
- useSessionList 接受 visible：非活动 tab 切 no-op subscribe，
  停止 live session-list churn 重渲染隐藏面板（better-sidebar
  'live views pause otherwise' 契约 = auto-collapse）
- tests/tabs.spec.ts：新增 5 个 badge 契约测试（6→11），mock
  sessions feed 直测 badge 纯函数
- AGENTS.md：Phase 2 标 partial（per-tab state / scratch 冒烟 /
  apps·messages·profile feed 延后，better-sidebar 0.18.0 无相应 API/数据源）

门禁：typecheck rc=0 · build rc=0（client.js 15.74→20K）· test 25/25

src/client/index.tsx

@@ -49,10 +49,43 @@ const TABS = {
  */
 type ApesClientContext = Context
 
-/** Read one client session list snapshot uSES-safely. */
-function useSessionList(ctx: Context) {
+/**
+ * Read the client session list uSES-safely, with `visible`-gated pausing
+ * (Phase 2 auto-collapse). `useSyncExternalStore` re-subscribes whenever the
+ * `subscribe` identity changes, so passing a no-op subscribe while the tab is
+ * not the active-open one stops live session-list churn from re-rendering a
+ * hidden panel — exactly better-sidebar's "live views pause otherwise"
+ * contract. The snapshot itself is always read (cheap), so a hidden tab still
+ * shows its last-known data when re-shown.
+ */
+const NOOP_SUBSCRIBE = () => () => {}
+function useSessionList(ctx: Context, visible: boolean) {
   const list = ctx.sessions.list
-  return useSyncExternalStore(list.subscribe, list.getSnapshot, list.getSnapshot)
+  return useSyncExternalStore(
+    visible ? list.subscribe : NOOP_SUBSCRIBE,
+    list.getSnapshot,
+    list.getSnapshot,
+  )
+}
+
+/** Count of sessions whose agent is currently running (badge source). */
+function runningCount(ctx: Context): number {
+  const { byId } = ctx.sessions.list.getSnapshot()
+  let n = 0
+  for (const id in byId) {
+    if (byId[id]?.running) n++
+  }
+  return n
+}
+
+/** Count of subagent-origin sessions (badge source for apes:agents). */
+function subagentCount(ctx: Context): number {
+  const { byId } = ctx.sessions.list.getSnapshot()
+  let n = 0
+  for (const id in byId) {
+    if (byId[id]?.origin === 'subagent') n++
+  }
+  return n
 }
 
 /** A row in a list view: id, title, and optional flag chips. */
@@ -132,7 +165,7 @@ function Empty({ key: key }: { key: string }): ReactElement {
  */
 function TasksView(props: TabComponentProps): ReactElement {
   useApesLocale()
-  const list = useSessionList(props.ctx)
+  const list = useSessionList(props.ctx, props.visible)
   const rows = Object.values(list.byId)
   if (rows.length === 0) {
     return (
@@ -165,7 +198,7 @@ function TasksView(props: TabComponentProps): ReactElement {
  */
 function AgentsView(props: TabComponentProps): ReactElement {
   useApesLocale()
-  const list = useSessionList(props.ctx)
+  const list = useSessionList(props.ctx, props.visible)
   const children = Object.values(list.byId).filter((s) => s.origin === 'subagent')
   if (children.length === 0) {
     return (
@@ -256,8 +289,14 @@ function ProfileView(): ReactElement {
 /**
  * Build the five tab descriptors. Each `component` receives the real
  * better-sidebar `TabComponentProps` (ctx / store / scope / tab / visible).
- * `visible` is deliberately unused in Phase 1 (no polling yet); Phase 2
- * gates live feeds on it the way better-sidebar's subagent view does.
+ *
+ * Phase 2 additions:
+ * - `badge` on tasks/agents: a cheap count pill (running sessions / subagent
+ *   count). Called on every tab-bar render, so it reads the live sessions
+ *   snapshot synchronously and returns `null` when the count is 0 (hidden).
+ * - `visible` is now honored by the live views: `useSessionList` swaps to a
+ *   no-op subscribe when the tab is not the active-open one (auto-collapse —
+ *   hidden panels stop re-rendering on session-list churn).
  */
 function buildDescriptors(): TabDescriptor[] {
   return [
@@ -266,6 +305,11 @@ function buildDescriptors(): TabDescriptor[] {
       title: () => t('tab.tasks.title'),
       order: 90,
       single: true,
+      // Running-session count pill (99+ capped by the host; 0 → hidden).
+      badge: (ctx) => {
+        const n = runningCount(ctx)
+        return n === 0 ? null : n
+      },
       component: (props) => <TasksView {...props} />,
     },
     {
@@ -273,6 +317,11 @@ function buildDescriptors(): TabDescriptor[] {
       title: () => t('tab.agents.title'),
       order: 91,
       single: true,
+      // Active-subagent count pill (0 → hidden).
+      badge: (ctx) => {
+        const n = subagentCount(ctx)
+        return n === 0 ? null : n
+      },
       component: (props) => <AgentsView {...props} />,
     },
     {