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.rs

@@ -230,7 +230,7 @@ async fn request_handler(
                     config,
                     &mut ctx,
                     websocket,
-                    &cancel_map,
+                    cancel_map,
                     host,
                     endpoint_rate_limiter,
                 )