feat(ui): use Lighthouse icon and "Home" label in sidebar nav toggle

ui/components/ui/sidebar/menu.test.tsx

@@ -128,7 +128,7 @@ describe("SidebarNavigationModeToggle", () => {
     expect(pushMock).toHaveBeenCalledWith("/lighthouse");
   });
 
-  it("does not navigate when Browse mode is selected", async () => {
+  it("does not navigate when Home mode is selected", async () => {
     // Given
     const user = userEvent.setup();
     const onChange = vi.fn();
@@ -142,7 +142,7 @@ describe("SidebarNavigationModeToggle", () => {
     );
 
     // When
-    await user.click(screen.getByRole("button", { name: "Browse" }));
+    await user.click(screen.getByRole("button", { name: "Home" }));
 
     // Then
     expect(onChange).toHaveBeenCalledWith(SIDEBAR_NAVIGATION_MODE.BROWSE);

ui/components/ui/sidebar/navigation-mode-toggle.tsx

@@ -1,8 +1,9 @@
 "use client";
 
-import { Bot, LayoutDashboard } from "lucide-react";
+import { LayoutDashboard } from "lucide-react";
 import { useRouter } from "next/navigation";
 
+import { LighthouseIcon } from "@/components/icons/Icons";
 import {
   Tooltip,
   TooltipContent,
@@ -27,13 +28,13 @@ export function SidebarNavigationModeToggle({
   const modes = [
     {
       value: SIDEBAR_NAVIGATION_MODE.BROWSE,
-      label: "Browse",
+      label: "Home",
       icon: LayoutDashboard,
     },
     {
       value: SIDEBAR_NAVIGATION_MODE.CHAT,
       label: "Chat",
-      icon: Bot,
+      icon: LighthouseIcon,
     },
   ] as const;