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/ConsoleTabs.tsx

@@ -9,7 +9,7 @@
  * worktree is still the workspace home's prompt box) — plus a link to
  * Settings → Agents. Four tabs is the server's limit (`MAX_PANE_SLOT`). The
  * bar is the console's only header: Home (the workspace's home) at its left
- * end, `actions` (the workspace's Tools menu) at its right end. A click shows a tab in the focused pane, Ctrl/Cmd+click
+ * end, `actions` (the single pane's split menus) at its right end. A click shows a tab in the focused pane, Ctrl/Cmd+click
  * (on a tab or a `+` item) opens it in a split to the right, and a tab drags
  * onto the panes (`PaneGrid.tsx`); a tab another pane shows is marked. A
  * right-click on a tab opens the same actions as a menu (`ContextMenu`).
@@ -29,6 +29,31 @@ import { freeSlot } from "../lanes/WorkspaceHome";
 import { RunIcon, startPaneDrag } from "./PaneGrid";
 import { ContextMenu, MenuItem, MenuSeparator, useContextMenu } from "../ContextMenu";
 
+type AiToolsState = ReturnType<typeof useAiTools>;
+
+/** The tools a new tab or split offers: the workspace's own whatever its
+ *  state, then every installed, enabled one. */
+export function newTabTools(lane: Lane, aiTools: AiToolsState): string[] {
+  return [
+    ...new Set([
+      lane.tool,
+      ...aiTools.tools.filter((x) => x.installed && x.enabled).map((x) => x.id),
+    ]),
+  ];
+}
+
+/** The start body of a bare tool on its default model, no prompt. Only a
+ *  different tool is named, as the home does: the workspace's own keeps
+ *  starting even once disabled. */
+export function newTabBody(id: string, lane: Lane, aiTools: AiToolsState) {
+  const model = aiTools.byId(id)?.defaultModel;
+  return {
+    prompt: "",
+    ...(id !== lane.tool ? { tool: id } : {}),
+    ...(model ? { model } : {}),
+  };
+}
+
 export function ConsoleTabs({
   lane,
   tabs,
@@ -52,7 +77,7 @@ export function ConsoleTabs({
   onClosed: (runId: string) => void;
   /** The workspace's home (its prompt box, Recents, context). */
   onHome?: () => void;
-  /** Right end of the bar (the workspace's Tools menu). */
+  /** Right end of the bar (the single pane's split menus). */
   actions?: ReactNode;
 }) {
   const { t } = useTranslation("lanes");
@@ -79,13 +104,7 @@ export function ConsoleTabs({
 
   const slot = freeSlot(lane.id, tabs);
   const label = (r: RunHandle) => (r.tool === "shell" ? t("tabs.terminal") : aiTools.label(r.tool));
-  // The workspace's own tool whatever its state, then every installed, enabled one.
-  const toolIds = [
-    ...new Set([
-      lane.tool,
-      ...aiTools.tools.filter((x) => x.installed && x.enabled).map((x) => x.id),
-    ]),
-  ];
+  const toolIds = newTabTools(lane, aiTools);
 
   const open = async (body: Record<string, unknown>, split = false) => {
     setMenuOpen(false);
@@ -217,33 +236,19 @@ export function ConsoleTabs({
               {t("tabs.newTerminal")}
             </button>
             <div className="my-1.5 border-t border-border" />
-            {toolIds.map((id) => {
-              const model = aiTools.byId(id)?.defaultModel;
-              return (
-                <button
-                  key={id}
-                  type="button"
-                  role="menuitem"
-                  data-testid={`console-tab-new-${id}`}
-                  className={item}
-                  onClick={(e) =>
-                    void open(
-                      {
-                        prompt: "",
-                        // Only a different tool is named, as the home does: the
-                        // workspace's own keeps starting even once disabled.
-                        ...(id !== lane.tool ? { tool: id } : {}),
-                        ...(model ? { model } : {}),
-                      },
-                      e.ctrlKey || e.metaKey
-                    )
-                  }
-                >
-                  <AiToolIcon tool={{ id, label: aiTools.label(id) }} className="h-4 w-4 !p-0" />
-                  {aiTools.label(id)}
-                </button>
-              );
-            })}
+            {toolIds.map((id) => (
+              <button
+                key={id}
+                type="button"
+                role="menuitem"
+                data-testid={`console-tab-new-${id}`}
+                className={item}
+                onClick={(e) => void open(newTabBody(id, lane, aiTools), e.ctrlKey || e.metaKey)}
+              >
+                <AiToolIcon tool={{ id, label: aiTools.label(id) }} className="h-4 w-4 !p-0" />
+                {aiTools.label(id)}
+              </button>
+            ))}
             <div className="my-1.5 border-t border-border" />
             <button
               type="button"