fix(control-ui): link dashboard breadcrumb

Make the topbar OpenClaw breadcrumb a semantic Overview link, wire the existing navigate event at the app shell, and preserve prefixed Control UI base paths.\n\nValidation:\n- pnpm test ui/src/ui/navigation.browser.test.ts\n- pnpm exec oxfmt --check --threads=1 ui/src/ui/components/dashboard-header.ts ui/src/ui/app-render.ts ui/src/ui/navigation.browser.test.ts\n- git diff --check origin/main...HEAD

ui/src/styles/layout.css

@@ -160,6 +160,23 @@
   color: var(--muted);
 }
 
+.topnav-shell .dashboard-header__breadcrumb-link {
+  display: inline-flex;
+  align-items: center;
+  margin: -2px -4px;
+  padding: 2px 4px;
+  border-radius: var(--radius-sm);
+  text-decoration: none;
+  white-space: nowrap;
+}
+
+.topnav-shell .dashboard-header__breadcrumb-link:hover,
+.topnav-shell .dashboard-header__breadcrumb-link:focus-visible {
+  color: var(--text);
+  text-decoration: underline;
+  text-underline-offset: 3px;
+}
+
 .topnav-shell .dashboard-header__breadcrumb-current {
   color: var(--accent);
   font-weight: 650;

ui/src/ui/app-render.ts

@@ -117,7 +117,13 @@ import {
 import { buildExternalLinkRel, EXTERNAL_LINK_TARGET } from "./external-link.ts";
 import { icons } from "./icons.ts";
 import { createLazyView, renderLazyView } from "./lazy-view.ts";
-import { normalizeBasePath, TAB_GROUPS, subtitleForTab, titleForTab } from "./navigation.ts";
+import {
+  normalizeBasePath,
+  TAB_GROUPS,
+  subtitleForTab,
+  titleForTab,
+  type Tab,
+} from "./navigation.ts";
 import { isPluginEnabledInConfigSnapshot } from "./plugin-activation.ts";
 import "./components/dashboard-header.ts";
 import {
@@ -1346,7 +1352,13 @@ export function renderApp(state: AppViewState) {
             <span class="nav-collapse-toggle__icon" aria-hidden="true">${icons.menu}</span>
           </button>
           <div class="topnav-shell__content">
-            <dashboard-header .tab=${state.tab}></dashboard-header>
+            <dashboard-header
+              .tab=${state.tab}
+              .basePath=${state.basePath}
+              @navigate=${(event: CustomEvent<Tab>) => {
+                state.setTab(event.detail);
+              }}
+            ></dashboard-header>
           </div>
           <div class="topnav-shell__actions">
             <button

ui/src/ui/components/dashboard-header.ts

@@ -1,6 +1,6 @@
 import { LitElement, html } from "lit";
 import { property } from "lit/decorators.js";
-import { titleForTab, type Tab } from "../navigation.js";
+import { pathForTab, titleForTab, type Tab } from "../navigation.js";
 
 export class DashboardHeader extends LitElement {
   override createRenderRoot() {
@@ -8,6 +8,24 @@ export class DashboardHeader extends LitElement {
   }
 
   @property() tab: Tab = "overview";
+  @property() basePath = "";
+
+  private handleOverviewClick(event: MouseEvent) {
+    if (
+      event.defaultPrevented ||
+      event.button !== 0 ||
+      event.metaKey ||
+      event.ctrlKey ||
+      event.shiftKey ||
+      event.altKey
+    ) {
+      return;
+    }
+    event.preventDefault();
+    this.dispatchEvent(
+      new CustomEvent("navigate", { detail: "overview", bubbles: true, composed: true }),
+    );
+  }
 
   override render() {
     const label = titleForTab(this.tab);
@@ -15,15 +33,13 @@ export class DashboardHeader extends LitElement {
     return html`
       <div class="dashboard-header">
         <div class="dashboard-header__breadcrumb">
-          <span
+          <a
             class="dashboard-header__breadcrumb-link"
-            @click=${() =>
-              this.dispatchEvent(
-                new CustomEvent("navigate", { detail: "overview", bubbles: true, composed: true }),
-              )}
+            href=${pathForTab("overview", this.basePath)}
+            @click=${this.handleOverviewClick}
           >
             OpenClaw
-          </span>
+          </a>
           <span class="dashboard-header__breadcrumb-sep">›</span>
           <span class="dashboard-header__breadcrumb-current">${label}</span>
         </div>

ui/src/ui/navigation.browser.test.ts

@@ -48,6 +48,34 @@ describe("control UI routing", () => {
     expect(dreamsLink).not.toBeNull();
   });
 
+  it("renders the dashboard breadcrumb as an overview link", async () => {
+    const app = mountApp("/channels");
+    await app.updateComplete;
+
+    const breadcrumb = app.querySelector<HTMLAnchorElement>(
+      "dashboard-header .dashboard-header__breadcrumb-link",
+    );
+    expect(breadcrumb).toBeInstanceOf(HTMLAnchorElement);
+    expect(breadcrumb?.getAttribute("href")).toBe("/overview");
+
+    breadcrumb?.dispatchEvent(new MouseEvent("click", { bubbles: true, cancelable: true }));
+    await app.updateComplete;
+
+    expect(app.tab).toBe("overview");
+    expect(window.location.pathname).toBe("/overview");
+  });
+
+  it("keeps the dashboard breadcrumb link inside the configured base path", async () => {
+    const app = mountApp("/ui/channels");
+    await app.updateComplete;
+
+    const breadcrumb = app.querySelector<HTMLAnchorElement>(
+      "dashboard-header .dashboard-header__breadcrumb-link",
+    );
+    expect(breadcrumb).toBeInstanceOf(HTMLAnchorElement);
+    expect(breadcrumb?.getAttribute("href")).toBe("/ui/overview");
+  });
+
   it("renders the dreaming view on the /dreaming route", async () => {
     const app = mountApp("/dreaming");
     app.dreamingStatus = {