Hello Christophe,
If you get a ‘SQLException: Connection refused’ then it seems like DB isn't reachable at all. Could you please check if you can reach out to the IP from your pods? If you get anything else in the error, please provide the screenshot of the error attached with this post removing all sensitive information.
I have found this documentation which explains how to connect to Cloud SQL from External Applications. I would recommend to check this and try to establish a connection from your java application using the instructions.
[1] https://cloud.google.com/sql/docs/mysql/connect-external-app#languages