feat(workspace): split menus start AI tools; drop the Tools menu

A pane's split right/down menus offered only New terminal. They now list
the same AI tools as the tab bar's + menu (newTabTools/newTabBody,
shared from ConsoleTabs), started bare in the first free slot on that
side of the pane.

The tab bar's Tools menu is gone: its readme run hit 409 ERUNLIVE
whenever slot 0 was live (always, in the session view) and depended on
a personal skill; MCP sync and the dev-sync check served the dormant
ship-feature-lane pipeline. The sidebar row menu's readme item goes too.
The routes stay, reached by `agenthub lanes mcp sync` and
`agenthub lanes sync-base`.

Also: the home's Memory header and file tabs no longer shrink (a long
file squeezed the tab row and clipped it).

client/src/components/run/PaneGrid.tsx

@@ -17,16 +17,7 @@
 
 import { useCallback, useEffect, useRef, useState, type ReactNode } from "react";
 import { useTranslation } from "react-i18next";
-import {
-  Check,
-  ChevronDown,
-  Columns2,
-  GripVertical,
-  Plus,
-  Rows2,
-  SquareTerminal,
-  X,
-} from "lucide-react";
+import { Check, ChevronDown, Columns2, GripVertical, Rows2, SquareTerminal, X } from "lucide-react";
 import type { RunHandle } from "../../lib/api";
 import { ContextMenu, MenuItem, MenuSeparator, useContextMenu } from "../ContextMenu";
 import {
@@ -174,7 +165,7 @@ const ITEM =
   "flex w-full items-center gap-2.5 rounded-md px-2.5 py-1.5 text-left text-sm text-fg-secondary hover:bg-surface-4 hover:text-fg-primary";
 
 /** A pane's split-right / split-down menus: move a hidden run beside
- *  `slot`, or start a new terminal there. In a pane header when the view is
+ *  `slot`, or start a new terminal or AI tool there. In a pane header when the view is
  *  split, beside Tools in the tab bar while one pane is shown. */
 export function SplitMenus({
   slot,
@@ -183,6 +174,8 @@ export function SplitMenus({
   label,
   onChange,
   canStart,
+  tools,
+  toolLabel,
   onNewSplit,
 }: {
   slot: number;
@@ -192,7 +185,11 @@ export function SplitMenus({
   label: (r: RunHandle) => string;
   onChange: LayoutUpdate;
   canStart: boolean;
-  onNewSplit: (target: number, edge: Edge) => void;
+  /** AI tool ids a new split can start, beside the terminal. */
+  tools: string[];
+  toolLabel: (id: string) => string;
+  /** `tool`: an AI tool id; none — a terminal. */
+  onNewSplit: (target: number, edge: Edge, tool?: string) => void;
 }) {
   const { t } = useTranslation("lanes");
   const full = shown.length >= MAX_PANES;
@@ -246,9 +243,27 @@ export function SplitMenus({
                   onNewSplit(slot, edge);
                 }}
               >
-                <Plus className="h-4 w-4" />
+                <SquareTerminal className="h-4 w-4" />
                 {t("panes.newTerminal")}
               </button>
+              {tools.map((id) => (
+                <button
+                  key={id}
+                  type="button"
+                  role="menuitem"
+                  data-testid={`pane-split-new-${edge}-${slot}-${id}`}
+                  disabled={!canStart}
+                  title={canStart ? undefined : t("tabs.full")}
+                  className={`${ITEM} disabled:opacity-40 disabled:hover:bg-transparent`}
+                  onClick={() => {
+                    close();
+                    onNewSplit(slot, edge, id);
+                  }}
+                >
+                  <AiToolIcon tool={{ id, label: toolLabel(id) }} className="h-4 w-4 !p-0" />
+                  {toolLabel(id)}
+                </button>
+              ))}
             </>
           )}
         </PaneMenu>
@@ -265,6 +280,8 @@ export function PaneGrid({
   renderPane,
   onChange,
   canStart,
+  tools,
+  toolLabel,
   onNewSplit,
 }: {
   layout: PaneLayout;
@@ -277,8 +294,11 @@ export function PaneGrid({
   onChange: LayoutUpdate;
   /** A slot is free for a new terminal. */
   canStart: boolean;
-  /** Start a new terminal into a split of `target`. */
-  onNewSplit: (target: number, edge: Edge) => void;
+  /** AI tool ids a new split can start, beside the terminal. */
+  tools: string[];
+  toolLabel: (id: string) => string;
+  /** Start a new terminal (or AI tool) into a split of `target`. */
+  onNewSplit: (target: number, edge: Edge, tool?: string) => void;
 }) {
   const { t } = useTranslation("lanes");
   const gridRef = useRef<HTMLDivElement>(null);
@@ -450,6 +470,8 @@ export function PaneGrid({
                     label={label}
                     onChange={onChange}
                     canStart={canStart}
+                    tools={tools}
+                    toolLabel={toolLabel}
                     onNewSplit={onNewSplit}
                   />
                   <button