fix(proxy): Log errors from the local proxy in auth-broker (#10659)

Handle errors from local proxy by parsing HTTP response in auth broker
code

Closes [#19476](https://github.com/neondatabase/cloud/issues/19476)

proxy/src/auth/backend/mod.rs

@@ -108,6 +108,10 @@ impl<T> Backend<'_, T> {
             Self::Local(_) => panic!("Local backend has no API"),
         }
     }
+
+    pub(crate) fn is_local_proxy(&self) -> bool {
+        matches!(self, Self::Local(_))
+    }
 }
 
 impl<'a, T> Backend<'a, T> {