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/layout.css

@@ -1,15 +1,20 @@
 /**
- * Layout push: when the sidebar is open it OCCUPIES the layout instead of
+ * Layout push: when a panel is open it OCCUPIES the layout instead of
  * floating over it — the app shell (#root, the AppFrame three-column grid)
- * gives up the panel's width on the right. Only the center column is
- * flexible (1fr), so the squeeze lands exactly on the conversation output
- * and the input bar, like a VSCode sidebar. The fixed panel covers the
- * vacated strip, which looks seamless because #root's background is the
- * theme base.
+ * gives up space. Only the center column is flexible (1fr), so the right
+ * panel's width squeeze (margin-right on #root) lands exactly on the
+ * conversation output and the input bar, like a VSCode sidebar.
  *
- * The width rides a CSS variable updated by the Sidebar shell (0 while
- * collapsed); expand/collapse animates both the margin and the panel slide
- * on the same theme duration. Width drags disable the transition so the
+ * The bottom panel squeezes ONLY the center column — it must not cover the
+ * app's own left sidebar or the right panel. The AppFrame's grid items are
+ * (#root > div > div:nth-child(2)): sidebarCol, centerCol, detailsCol, so
+ * the vertical push lands on the center column alone. The fixed panels
+ * cover the vacated strips, which looks seamless because #root's background
+ * is the theme base.
+ *
+ * The sizes ride CSS variables updated by the Sidebar shell (0 while
+ * collapsed); expand/collapse animates both the margins and the panel
+ * slides on the same theme duration. Drags disable the transition so the
  * layout tracks the pointer.
  */
 #root {
@@ -17,12 +22,23 @@
   transition: margin-right var(--ds-transition-duration-slow) var(--ds-ease-in-out);
 }
 
-body[data-dsh-sidebar-dragging] #root {
+/* The AppFrame's grid items are sidebarCol, centerCol, detailsCol (children
+   1-3 of #root > div) — nth-child(2) is the center column. A stretched grid
+   item shrinks by its margins, so the conversation content (output + input
+   bar) lifts without touching the sidebars. */
+#root > div > div:nth-child(2) {
+  margin-bottom: var(--dsh-sidebar-height, 0px);
+  transition: margin-bottom var(--ds-transition-duration-slow) var(--ds-ease-in-out);
+}
+
+body[data-dsh-sidebar-dragging] #root,
+body[data-dsh-sidebar-dragging] #root > div > div:nth-child(2) {
   transition: none;
 }
 
 @media (prefers-reduced-motion: reduce) {
-  #root {
+  #root,
+  #root > div > div:nth-child(2) {
     transition: none;
   }
 }