feat(web): polish master chat with model selector, params config, and empty state (#519)

Co-authored-by: Jason Woltje <jason@diversecanvas.com>
Co-committed-by: Jason Woltje <jason@diversecanvas.com>

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

@@ -164,6 +164,27 @@ export function ChatOverlay(): React.JSX.Element {
 
           {/* Header Controls */}
           <div className="flex items-center gap-1">
+            {/* New Conversation Button */}
+            <button
+              onClick={() => {
+                chatRef.current?.startNewConversation(null);
+              }}
+              className="rounded p-1.5 transition-colors hover:bg-black/5 focus:outline-none focus:ring-2"
+              aria-label="New conversation"
+              title="New conversation (Cmd+N)"
+            >
+              <svg
+                className="h-4 w-4"
+                style={{ color: "rgb(var(--text-secondary))" }}
+                fill="none"
+                viewBox="0 0 24 24"
+                stroke="currentColor"
+                strokeWidth={2}
+              >
+                <path d="M12 4v16m8-8H4" />
+              </svg>
+            </button>
+
             {/* Minimize Button */}
             <button
               onClick={minimize}