chore: update LazyRefresh cache

Author: jackwotherspoon

google/cloud/sql/connector/instance.py

@@ -55,7 +55,7 @@ def __init__(
         """Initializes a RefreshAheadCache instance.
 
         Args:
-            conn_name (ConnectionName): The Cloud SQL Instance's
+            conn_name (ConnectionName): The Cloud SQL instance's
                 connection name.
             client (CloudSQLClient): The Cloud SQL Client instance.
             keys (asyncio.Future): A future to the client's public-private key

google/cloud/sql/connector/lazy.py

@@ -38,25 +38,23 @@ class LazyRefreshCache:
 
     def __init__(
         self,
-        instance_connection_string: str,
+        conn_name: str,
         client: CloudSQLClient,
         keys: asyncio.Future,
         enable_iam_auth: bool = False,
     ) -> None:
         """Initializes a LazyRefreshCache instance.
 
         Args:
-            instance_connection_string (str): The Cloud SQL Instance's
-                connection string (also known as an instance connection name).
+            conn_name (ConnectionName): The Cloud SQL instance's
+                connection name.
             client (CloudSQLClient): The Cloud SQL Client instance.
             keys (asyncio.Future): A future to the client's public-private key
                 pair.
             enable_iam_auth (bool): Enables automatic IAM database authentication
                 (Postgres and MySQL) as the default authentication method for all
                 connections.
         """
-        # validate and parse instance connection name
-        conn_name = _parse_instance_connection_name(instance_connection_string)
         self._project, self._region, self._instance = (
             conn_name.project,
             conn_name.region,