Connection issue with neon DB and FastAPI application deployed on Vercel

pool = None
@asynccontextmanager
async def lifespan(app: FastAPI):
    global pool
    pool = await asyncpg.create_pool(os.getenv('DATABASE_URL'))
    yield
    if pool:
        await pool.close()
app = FastAPI(lifespan=lifespan)

pool = None
async def startup_event():
    global pool
    logging.info("Startup event: Initializing database pool")
    pool = await asyncpg.create_pool(os.getenv('DATABASE_URL'))
    logging.info(f"Startup event: Database pool initialized: {pool}")

async def shutdown_event():
    global pool
    logging.info("Shutdown event: Initiated")
    if pool:
        logging.info("Shutdown event: Closing database pool")
        await pool.close()
        logging.info("Shutdown event: Database pool closed")

app = FastAPI()
app.add_event_handler("startup", startup_event)
app.add_event_handler("shutdown", shutdown_event)