flatten proxy flow (#6447)

## Problem

Taking my ideas from https://github.com/neondatabase/neon/pull/6283 and
doing a bit less radical changes. smaller commits.

Proxy flow was quite deeply nested, which makes adding more interesting
error handling quite tricky.

## Summary of changes

I recommend reviewing commit by commit.

1. move handshake logic into a separate file
2. move passthrough logic into a separate file
3. no longer accept a closure in CancelMap session logic
4. Remove connect_to_db, copy logic into handle_client
5. flatten auth_and_wake_compute in authenticate
6. record info for link auth

proxy/src/serverless/websocket.rs

@@ -133,7 +133,7 @@ pub async fn serve_websocket(
     config: &'static ProxyConfig,
     ctx: &mut RequestMonitoring,
     websocket: HyperWebsocket,
-    cancel_map: &CancelMap,
+    cancel_map: Arc<CancelMap>,
     hostname: Option<String>,
     endpoint_rate_limiter: Arc<EndpointRateLimiter>,
 ) -> anyhow::Result<()> {