proxy: spawn cancellation checks in the background (#9918)

## Problem
For cancellation, a connection is open during all the cancel checks.
## Summary of changes
Spawn cancellation checks in the background, and close connection
immediately.
Use task_tracker for cancellation checks.

proxy/src/serverless/websocket.rs

@@ -123,6 +123,7 @@ impl<S: AsyncRead + AsyncWrite + Unpin> AsyncBufRead for WebSocketRw<S> {
     }
 }
 
+#[allow(clippy::too_many_arguments)]
 pub(crate) async fn serve_websocket(
     config: &'static ProxyConfig,
     auth_backend: &'static crate::auth::Backend<'static, ()>,
@@ -131,6 +132,7 @@ pub(crate) async fn serve_websocket(
     cancellation_handler: Arc<CancellationHandlerMain>,
     endpoint_rate_limiter: Arc<EndpointRateLimiter>,
     hostname: Option<String>,
+    cancellations: tokio_util::task::task_tracker::TaskTracker,
 ) -> anyhow::Result<()> {
     let websocket = websocket.await?;
     let websocket = WebSocketServer::after_handshake(TokioIo::new(websocket));
@@ -149,6 +151,7 @@ pub(crate) async fn serve_websocket(
         ClientMode::Websockets { hostname },
         endpoint_rate_limiter,
         conn_gauge,
+        cancellations,
     ))
     .await;