feat: Add "New Chat" button to reset chat session in-place

Adds startNewSession() to useChatSession hook that closes the current
session without closing the panel. New Plus button in chat header
appears when a conversation exists, with shift+click to skip confirm.

apps/web/src/components/chat/ChatSlideOver.tsx

@@ -1,6 +1,6 @@
 import { useEffect, useRef } from 'react';
 import { motion, AnimatePresence } from 'motion/react';
-import { X, Loader2, AlertTriangle, RotateCcw } from 'lucide-react';
+import { X, Plus, Loader2, AlertTriangle, RotateCcw } from 'lucide-react';
 import { Button } from '@/components/ui/button';
 import { useChatSession } from '@/hooks/useChatSession';
 import { ChatBubble } from './ChatBubble';
@@ -42,7 +42,7 @@ function ChatSlideOverInner({
   initiativeId: string;
   onClose: () => void;
 }) {
-  const { messages, agentStatus, agentError, sendMessage, retryLastMessage, closeSession, isSending } =
+  const { session, messages, agentStatus, agentError, sendMessage, retryLastMessage, closeSession, startNewSession, isSending } =
     useChatSession(target.type, target.id, initiativeId);
 
   const scrollRef = useRef<HTMLDivElement>(null);
@@ -105,6 +105,19 @@ function ChatSlideOverInner({
               Processing...
             </div>
           )}
+          {session && messages.length > 0 && (
+            <button
+              className="shrink-0 rounded-md p-1 text-muted-foreground transition-colors hover:bg-accent hover:text-foreground disabled:pointer-events-none disabled:opacity-50"
+              title="New Chat"
+              disabled={isAgentWorking}
+              onClick={(e) => {
+                if (!e.shiftKey && !window.confirm('Start a new chat? The current conversation will be closed.')) return;
+                startNewSession();
+              }}
+            >
+              <Plus className="h-4 w-4" />
+            </button>
+          )}
           <button
             className="shrink-0 rounded-md p-1 text-muted-foreground transition-colors hover:bg-accent hover:text-foreground"
             onClick={handleClose}

apps/web/src/hooks/useChatSession.ts

@@ -32,6 +32,7 @@ export interface UseChatSessionResult {
   sendMessage: (message: string) => void;
   retryLastMessage: () => void;
   closeSession: () => void;
+  startNewSession: () => void;
   isSending: boolean;
   isLoading: boolean;
 }
@@ -186,6 +187,13 @@ export function useChatSession(
     }
   }, []);
 
+  const startNewSession = useCallback(() => {
+    const s = sessionRef.current;
+    if (!s) return;
+    closeMutateRef.current({ sessionId: s.id });
+    setOptimisticMessages([]);
+  }, []);
+
   const isLoading = sessionQuery.isLoading;
   const isSending = sendMutation.isPending;
 
@@ -197,6 +205,7 @@ export function useChatSession(
     sendMessage,
     retryLastMessage,
     closeSession,
+    startNewSession,
     isSending,
     isLoading,
   };