feat(demo): setup /demo mount and copy demo HTML

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

app.py

@@ -106,6 +106,7 @@ async def add_no_cache_header(request: Request, call_next):
         response.headers["Expires"] = "0"
     return response
 
+app.mount("/demo", StaticFiles(directory="demo", html=True), name="demo")
 _FRONTEND_DIR = Path(__file__).with_name("frontend")
 if _FRONTEND_DIR.exists():
     app.mount("/app", StaticFiles(directory=_FRONTEND_DIR, html=True), name="frontend")