since we're dealing with different tests, try this

Author: glasnt

cloud-sql/sqlserver/tedious/ci-setup.json

@@ -6,8 +6,7 @@
       "CLOUD_SQL_CONNECTION_NAME": "$INSTANCE_CONNECTION_NAME",
       "INSTANCE_UNIX_SOCKET": "$UNIX_SOCKET_DIR/$INSTANCE_CONNECTION_NAME",
       "DB_NAME": "kokoro_ci",
-      "DB_USER": "kokoro_ci",
-      "PRIVATE_IP": "true"
+      "DB_USER": "kokoro_ci"
     },
     "secrets": {
       "DB_PASS": "nodejs-docs-samples-tests/nodejs-docs-samples-sql-password"

cloud-sql/sqlserver/tedious/test/server.test.js

@@ -24,10 +24,12 @@ const serverConnector = require(SAMPLE_PATH);
 
 const _instance_connect_backup = process.env.INSTANCE_CONNECTION_NAME;
 delete process.env.INSTANCE_CONNECTION_NAME;
+process.env.PRIVATE_IP = "true"
 
 const serverTcp = require(SAMPLE_PATH);
 
 process.env.INSTANCE_CONNECTION_NAME = _instance_connect_backup;
+process.env.PRIVATE_IP = ""
 
 after(() => {
   serverTcp.close();