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/auth/backend/link.rs

@@ -1,6 +1,7 @@
 use crate::{
     auth, compute,
     console::{self, provider::NodeInfo},
+    context::RequestMonitoring,
     error::UserFacingError,
     stream::PqStream,
     waiters,
@@ -54,6 +55,7 @@ pub fn new_psql_session_id() -> String {
 }
 
 pub(super) async fn authenticate(
+    ctx: &mut RequestMonitoring,
     link_uri: &reqwest::Url,
     client: &mut PqStream<impl AsyncRead + AsyncWrite + Unpin>,
 ) -> auth::Result<NodeInfo> {
@@ -94,6 +96,10 @@ pub(super) async fn authenticate(
         .dbname(&db_info.dbname)
         .user(&db_info.user);
 
+    ctx.set_user(db_info.user.into());
+    ctx.set_project(db_info.aux.clone());
+    tracing::Span::current().record("ep", &tracing::field::display(&db_info.aux.endpoint_id));
+
     // Backwards compatibility. pg_sni_proxy uses "--" in domain names
     // while direct connections do not. Once we migrate to pg_sni_proxy
     // everywhere, we can remove this.