Proxy refactor auth+connect (#6708)

## Problem

Not really a problem, just refactoring.

## Summary of changes

Separate authenticate from wake compute.

Do not call wake compute second time if we managed to connect to
postgres or if we got it not from cache.

proxy/src/error.rs

@@ -29,7 +29,7 @@ pub trait UserFacingError: ReportableError {
     }
 }
 
-#[derive(Copy, Clone, Debug)]
+#[derive(Copy, Clone, Debug, Eq, PartialEq)]
 pub enum ErrorKind {
     /// Wrong password, unknown endpoint, protocol violation, etc...
     User,
@@ -90,3 +90,13 @@ impl ReportableError for tokio::time::error::Elapsed {
         ErrorKind::RateLimit
     }
 }
+
+impl ReportableError for tokio_postgres::error::Error {
+    fn get_error_kind(&self) -> ErrorKind {
+        if self.as_db_error().is_some() {
+            ErrorKind::Postgres
+        } else {
+            ErrorKind::Compute
+        }
+    }
+}