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/pages/Chat/ChatToolbar.tsx

@@ -1,8 +1,9 @@
 /**
  * Chat Toolbar
- * Session selector, refresh, and thinking toggle controls.
+ * Session selector, new session, refresh, and thinking toggle.
+ * Rendered in the Header when on the Chat page.
  */
-import { RefreshCw, Brain, ChevronDown } from 'lucide-react';
+import { RefreshCw, Brain, ChevronDown, Plus } from 'lucide-react';
 import { Button } from '@/components/ui/button';
 import { useChatStore } from '@/stores/chat';
 import { cn } from '@/lib/utils';
@@ -11,6 +12,7 @@ export function ChatToolbar() {
   const sessions = useChatStore((s) => s.sessions);
   const currentSessionKey = useChatStore((s) => s.currentSessionKey);
   const switchSession = useChatStore((s) => s.switchSession);
+  const newSession = useChatStore((s) => s.newSession);
   const refresh = useChatStore((s) => s.refresh);
   const loading = useChatStore((s) => s.loading);
   const showThinking = useChatStore((s) => s.showThinking);
@@ -51,6 +53,17 @@ export function ChatToolbar() {
         <ChevronDown className="absolute right-2 top-1/2 -translate-y-1/2 h-3.5 w-3.5 text-muted-foreground pointer-events-none" />
       </div>
 
+      {/* New Session */}
+      <Button
+        variant="ghost"
+        size="icon"
+        className="h-8 w-8"
+        onClick={newSession}
+        title="New session"
+      >
+        <Plus className="h-4 w-4" />
+      </Button>
+
       {/* Refresh */}
       <Button
         variant="ghost"

src/pages/Chat/index.tsx

@@ -10,7 +10,6 @@ import { Card, CardContent } from '@/components/ui/card';
 import { useChatStore } from '@/stores/chat';
 import { useGatewayStore } from '@/stores/gateway';
 import { LoadingSpinner } from '@/components/common/LoadingSpinner';
-import { ChatToolbar } from './ChatToolbar';
 import { ChatMessage } from './ChatMessage';
 import { ChatInput } from './ChatInput';
 import { extractText } from './message-utils';
@@ -63,13 +62,7 @@ export function Chat() {
   const streamText = streamingMessage ? extractText(streamingMessage) : '';
 
   return (
-    <div className="flex h-[calc(100vh-4rem)] flex-col">
-      {/* Toolbar: session selector, refresh, thinking toggle */}
-      <div className="flex items-center justify-between px-4 py-2 border-b">
-        <div /> {/* spacer */}
-        <ChatToolbar />
-      </div>
-
+    <div className="flex flex-col -m-6" style={{ height: 'calc(100vh - 3.5rem)' }}>
       {/* Messages Area */}
       <div className="flex-1 overflow-y-auto px-4 py-4">
         <div className="max-w-4xl mx-auto space-y-4">