Check if you are using MySQL 8.4. By default in Cloud SQL, Mysql 8.4 the caching_sha2_password auth plugin is the default. You may need to configure your go mysql client to use caching_sha2_password also.

It looks like you already found the article describing several ways to connect to a private-ip Cloud SQL instance. Just in case others find it useful also, here's the link: https://cloud.google.com/sql/docs/mysql/connect-to-instance-from-outside-vpc