proxy: pool connection logs (#5020)

## Problem

Errors and notices that happen during a pooled connection lifecycle have
no session identifiers

## Summary of changes

Using a watch channel, we set the session ID whenever it changes. This
way we can see the status of a connection for that session

Also, adding a connection id to be able to search the entire connection
lifecycle

proxy/src/auth/backend/classic.rs

@@ -62,7 +62,6 @@ pub(super) async fn authenticate(
         }
     };
 
-    info!("compute node's state has likely changed; requesting a wake-up");
     let mut num_retries = 0;
     let mut node = loop {
         let wake_res = api.wake_compute(extra, creds).await;