Build Verse: a poem-quote app on the agent-native chat template

Adds a Postgres-backed quotes domain (poems/quotes/favorites) exposed as
five agent-native actions (list-quotes, get-random-quote, create-quote,
toggle-favorite, list-favorites) callable from both chat and the React UI
via useActionQuery/useActionMutation. Moves the primary UI from chat to a
mobile-first Quotes/Favorites experience (chat moves to /chat), adds
manual OpenTelemetry instrumentation exporting traces/metrics/logs over
OTLP, and wires a local Docker Postgres for shared state.

app/components/layout/Layout.tsx

@@ -38,7 +38,7 @@ const SIDEBAR_COLLAPSE_KEY = "chat.sidebar.collapsed";
  */
 function routeOwnsToolbar(pathname: string): boolean {
   return (
-    pathname === "/" ||
+    pathname === "/chat" ||
     pathname.startsWith("/chat/") ||
     pathname === "/database" ||
     pathname.startsWith("/extensions")
@@ -52,7 +52,7 @@ export function Layout({ children }: LayoutProps) {
   const [mobileSidebarOpen, setMobileSidebarOpen] = useState(false);
   const [sidebarCollapsed, setSidebarCollapsed] = useState(true);
   const isChatRoute =
-    location.pathname === "/" || location.pathname.startsWith("/chat/");
+    location.pathname === "/chat" || location.pathname.startsWith("/chat/");
   const chatHomeHandoffActive = useAgentChatHomeHandoff({
     storageKey: "chat",
     activePath: location.pathname,
@@ -61,7 +61,7 @@ export function Layout({ children }: LayoutProps) {
   const chatHomeHandoffPending = isAgentChatHomeHandoffActive("chat");
   useAgentChatHomeHandoffLinks({
     storageKey: "chat",
-    isChatPath: (pathname) => pathname === "/" || pathname.startsWith("/chat/"),
+    isChatPath: (pathname) => pathname === "/chat" || pathname.startsWith("/chat/"),
     requireActiveHandoff: true,
   });
 
@@ -100,7 +100,7 @@ export function Layout({ children }: LayoutProps) {
   const ownsToolbar = routeOwnsToolbar(location.pathname);
   function openAskAgentFullscreen() {
     focusAgentChat();
-    navigateWithAgentChatViewTransition(navigate, "/");
+    navigateWithAgentChatViewTransition(navigate, "/chat");
   }
 
   const contentFrame = (