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/lanes/LaneCard.tsx

@@ -9,12 +9,7 @@
  * lane-detail section, whose header above it already shows them. Neither is
  * progress: the pipeline map directly below this card draws the same number
  * as named, coloured nodes, so a bar and a percent beside it were a worse
- * second telling of it. The repo
- * tooling dropdown (`LaneToolsMenu`, exported from this file — agents
- * install / MCP sync / dev-sync check / create-update readme) and the
- * remove-lane button live in Workspace's page header / pipeline-picker row
- * instead of here, so they stay reachable and un-clipped regardless of this
- * card's own scroll area. The working copy — branch, uncommitted counts, the
+ * second telling of it. The working copy — branch, uncommitted counts, the
  * git action bar — is not here either: it heads the Changes panel
  * (`LaneGitHeader`), beside the diff it describes.
  * @author Nguyễn Ngọc Trí Vĩ <vinnt@smartgift.vn>
@@ -116,144 +111,6 @@ export function since(sec: number | null): string {
   return `${Math.floor(sec / 3600)}h ${Math.floor((sec % 3600) / 60)}m`;
 }
 
-/**
- * Repo tooling (MCP sync / dev-sync check, and the
- * create/update-readme run, which moved here from the Add-lane modal) for one lane,
- * collapsed into a single dropdown. Lives outside LaneCard so it can be
- * placed in the Workspace page header, next to "Add lane" — it polls its
- * own runtime state independently of LaneCard's, same pattern as the
- * separately-polled git/locks facts elsewhere on this page.
- */
-export function LaneToolsMenu({ lane }: { lane: Lane }) {
-  const { t } = useTranslation(["lanes"]);
-  const [toolsMenuOpen, setToolsMenuOpen] = useState(false);
-  const [laneActionBusy, setLaneActionBusy] = useState<"mcp" | "sync-check" | "docs" | null>(null);
-  const [laneActionResult, setLaneActionResult] = useState<string | null>(null);
-  const runtime = useLaneRuntime(lane.id, 0);
-
-  const runLaneAction = async (which: "mcp" | "sync-check" | "docs", fn: () => Promise<string>) => {
-    setLaneActionBusy(which);
-    setLaneActionResult(null);
-    try {
-      setLaneActionResult(await fn());
-    } catch (err) {
-      setLaneActionResult(err instanceof Error ? err.message : String(err));
-    } finally {
-      setLaneActionBusy(null);
-    }
-  };
-
-  // A skill only exists inside a CLI session, so there is nothing server-side
-  // to call: this opens the lane's own terminal run with the slash command as
-  // its first message. Claude-only — codex has no slash commands.
-  const handleWriteDocs = () =>
-    runLaneAction("docs", async () => {
-      await api.run.start({
-        laneId: lane.id,
-        cwd: lane.cwd,
-        initialPrompt: "/sg-all:sg-md-writing",
-      });
-      return t("actions.writeDocsResult");
-    });
-
-  const handleMcpSync = () =>
-    runLaneAction("mcp", async () => {
-      const result = await api.lanes.mcpSync(lane.id);
-      return t("actions.mcpSyncResult", { servers: result.servers.join(", ") || "none" });
-    });
-
-  const handleSyncCheck = () =>
-    runLaneAction("sync-check", async () => {
-      const result = await api.lanes.syncBaseCheck(lane.id);
-      if (result.code === 5 && result.collisions && result.collisions.length > 0) {
-        const c = result.collisions[0]!;
-        return t("actions.syncCheckCollision", { file: c.file, suggestion: c.suggestion });
-      }
-      return t("actions.syncCheckClean", {
-        count: result.devDelta?.length ?? 0,
-        overlap: result.overlap?.length ? result.overlap.join(", ") : "none",
-      });
-    });
-
-  if (!runtime?.available) return null;
-
-  return (
-    <div className="relative">
-      <button
-        type="button"
-        data-testid="lane-tools-menu"
-        aria-haspopup="menu"
-        aria-expanded={toolsMenuOpen}
-        disabled={laneActionBusy !== null}
-        onClick={(e) => {
-          e.stopPropagation();
-          setToolsMenuOpen((v) => !v);
-        }}
-        className="rounded border border-border-light px-2 py-1 text-xs text-fg-secondary transition-colors hover:text-fg-primary disabled:opacity-50"
-      >
-        {laneActionBusy ? t("actions.busy") : t("actions.tools")}
-      </button>
-      {toolsMenuOpen && (
-        <div
-          role="menu"
-          className="absolute right-0 z-10 mt-1 min-w-44 overflow-hidden rounded-md border border-border-light bg-surface-0 py-1 shadow-lg shadow-black/40"
-        >
-          {lane.tool === "claude" && (
-            <button
-              type="button"
-              role="menuitem"
-              data-testid="lane-write-docs"
-              title={t("actions.writeDocsHint")}
-              onClick={(e) => {
-                e.stopPropagation();
-                setToolsMenuOpen(false);
-                void handleWriteDocs();
-              }}
-              className="block w-full px-3 py-1.5 text-left text-fg-secondary hover:bg-surface-2"
-            >
-              {t("actions.writeDocs")}
-            </button>
-          )}
-          <button
-            type="button"
-            role="menuitem"
-            data-testid="lane-mcp-sync"
-            onClick={(e) => {
-              e.stopPropagation();
-              setToolsMenuOpen(false);
-              void handleMcpSync();
-            }}
-            className="block w-full px-3 py-1.5 text-left text-fg-secondary hover:bg-surface-2"
-          >
-            {t("actions.mcpSync")}
-          </button>
-          <button
-            type="button"
-            role="menuitem"
-            data-testid="lane-sync-check"
-            onClick={(e) => {
-              e.stopPropagation();
-              setToolsMenuOpen(false);
-              void handleSyncCheck();
-            }}
-            className="block w-full px-3 py-1.5 text-left text-fg-secondary hover:bg-surface-2"
-          >
-            {t("actions.syncCheck")}
-          </button>
-        </div>
-      )}
-      {laneActionResult && (
-        <p
-          data-testid="lane-action-result"
-          className="absolute right-0 top-full mt-1 w-max max-w-xs truncate rounded border border-border-light bg-surface-0 px-2 py-1 text-[11px] text-fg-secondary shadow-lg shadow-black/40"
-        >
-          {laneActionResult}
-        </p>
-      )}
-    </div>
-  );
-}
-
 export default function LaneCard({
   lane,
   onAction,