fix(chat): move toolbar to Header and add New Session button

- Move ChatToolbar (session selector, refresh, thinking toggle) from
  the Chat page body into the Header component, so controls appear
  at the same level as the "Chat" title
- Add New Session button (+) to create a fresh conversation
- Add newSession action to chat store
- Header conditionally renders ChatToolbar only on /chat route
- Chat page fills full content area without duplicate toolbar

src/stores/chat.ts

@@ -60,6 +60,7 @@ interface ChatState {
   // Actions
   loadSessions: () => Promise<void>;
   switchSession: (key: string) => void;
+  newSession: () => void;
   loadHistory: () => Promise<void>;
   sendMessage: (text: string) => Promise<void>;
   handleChatEvent: (event: Record<string, unknown>) => void;
@@ -129,6 +130,23 @@ export const useChatStore = create<ChatState>((set, get) => ({
     get().loadHistory();
   },
 
+  // ── New session ──
+
+  newSession: () => {
+    // Generate a new unique session key and switch to it
+    const newKey = `session-${Date.now()}`;
+    set({
+      currentSessionKey: newKey,
+      messages: [],
+      streamingText: '',
+      streamingMessage: null,
+      activeRunId: null,
+      error: null,
+    });
+    // Reload sessions list to include the new one after first message
+    get().loadSessions();
+  },
+
   // ── Load chat history ──
 
   loadHistory: async () => {