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/pages/__tests__/Workspace.test.tsx

@@ -25,6 +25,7 @@ type LaneFixture = {
   detected_signal: string | null;
   run_id: string | null;
   active_feature_id?: number | null;
+  tool?: string;
 };
 
 let lanesToReturn: LaneFixture[] = [
@@ -806,6 +807,17 @@ describe("split panes", () => {
     expect(api.lanes.action).toHaveBeenCalledWith(1, "start", { slot: 2, shell: true });
   });
 
+  it("a split menu starts an AI tool, bare, in the first free slot", async () => {
+    lanesToReturn = lanesToReturn.map((l) => ({ ...l, tool: "claude" }));
+    withRuns([live(0), live(1)]);
+    await open("/workspace?lane=1&run=agenthub-lane-1");
+    await ctrlClick(screen.getByTestId("console-tab-1"));
+    const user = userEvent.setup();
+    await user.click(screen.getByTestId("pane-split-right-1"));
+    await user.click(screen.getByTestId("pane-split-new-right-1-claude"));
+    expect(api.lanes.action).toHaveBeenCalledWith(1, "start", { slot: 2, prompt: "" });
+  });
+
   it("with one pane, the split menus sit beside Tools and split it", async () => {
     withRuns([live(0), live(1)]);
     await open("/workspace?lane=1&run=agenthub-lane-1");