feat: 侧边栏双面板 — 右上角按钮簇、底部面板（首展自动终端/关闭按钮）、跨面板拖 Tab、拖动性能优化

- 右上角持久按钮簇：横向排列、独立 glyph（底栏/侧拉）、始终钉在视口右上角（侧边栏展开时位于其标签条右端，真实挤占 Tab 空间）
- 底部面板：独立工作台，只挤占中间 Agent 输出区（不覆盖左右侧边栏），右缘分割线、关闭 x、首展自动开终端（二级设置开关，默认开）
- 两面板拐角双向拖动调节尺寸；拖动改为 rAF 节流直写 DOM，消除卡顿；面板尺寸互钳制防丢失
- 跨面板拖 Tab（合并/拆分落点），moveTab/moveTabToEdge 支持跨树移动
- 欢迎卡片改响应式网格；布局/几何全部按会话持久化，旧状态平滑迁移

src/client/service.ts

@@ -379,7 +379,9 @@ function applyDedupe(state: SidebarState, tab: SidebarTab, descriptor: TabDescri
   const dedupeKey = descriptor.dedupeKey ?? (descriptor.single === true ? () => descriptor.id : undefined)
   const key = dedupeKey?.(tab)
   if (key !== undefined) {
-    for (const leaf of allLeaves(state.splits)) {
+    // The scan covers BOTH trees: opening a single-instance tab from the
+    // bottom panel focuses an existing instance wherever it lives.
+    for (const leaf of allLeaves(state.splits).concat(allLeaves(state.bottomSplits))) {
       const existing = leaf.tabs.find(t => t.type === tab.type && dedupeKey!(t) === key)
       if (existing !== undefined) return activateTab(state, leaf.id, existing.id)
     }
@@ -387,9 +389,9 @@ function applyDedupe(state: SidebarState, tab: SidebarTab, descriptor: TabDescri
   return openTabInActivePane(state, tab)
 }
 
-/** Find which pane hosts a tab id ('' if none). */
+/** Find which pane hosts a tab id ('' if none). Either tree is searched. */
 function findPaneIdOf(state: SidebarState, tabId: string): string {
-  for (const leaf of allLeaves(state.splits)) {
+  for (const leaf of allLeaves(state.splits).concat(allLeaves(state.bottomSplits))) {
     if (leaf.tabs.some(t => t.id === tabId)) return leaf.id
   }
   return state.activePane ?? ''