proxy: log params when no endpoint (#5418)

## Problem

Our SNI error dashboard features IP addresses but it's not immediately
clear who that is still (#5369)

## Summary of changes

Log some startup params with this error

proxy/src/auth/backend.rs

@@ -160,6 +160,19 @@ impl BackendType<'_, ClientCredentials<'_>> {
             Test(_) => Some("test".to_owned()),
         }
     }
+
+    /// Get username from the credentials.
+    pub fn get_user(&self) -> &str {
+        use BackendType::*;
+
+        match self {
+            Console(_, creds) => creds.user,
+            Postgres(_, creds) => creds.user,
+            Link(_) => "link",
+            Test(_) => "test",
+        }
+    }
+
     /// Authenticate the client via the requested backend, possibly using credentials.
     #[tracing::instrument(fields(allow_cleartext = allow_cleartext), skip_all)]
     pub async fn authenticate(

proxy/src/proxy.rs

@@ -697,7 +697,14 @@ impl<S: AsyncRead + AsyncWrite + Unpin> Client<'_, S> {
             .await
         {
             Ok(auth_result) => auth_result,
-            Err(e) => return stream.throw_error(e).await,
+            Err(e) => {
+                let user = creds.get_user();
+                let db = params.get("database");
+                let app = params.get("application_name");
+                let params_span = tracing::info_span!("", ?user, ?db, ?app);
+
+                return stream.throw_error(e).instrument(params_span).await;
+            }
         };
 
         let AuthSuccess {