Unable to connect Apps Script to Cloud SQL using JDBC

So... I have been trying to set up the connection to a Cloud SQL for MySQL database from an Apps Script function, however I am unable to figure out why it is not working. I have been following the documentation for JDBC, however no matter what I do, the connection always fails.

The following is the code I am using:

const connectionName = '<project_id>:<region>:<instance_id>';
const user = '<user>';
const userPwd = '<user_pass>';
const db = '<database>';

const dbUrl = 'jdbc:google:mysql://' + connectionName + '/' + db;

function connect() {
  const conn = Jdbc.getCloudSqlConnection(dbUrl, user, userPwd);

  let start = new Date();
  let stmt = conn.createStatement();

  stmt.setMaxRows(1000);

  let results = stmt.executeQuery('SELECT * FROM entries');
  let numCols = results.getMetaData().getColumnCount();

  while (results.next()) {
    let rowString = '';
    for (let col = 0; col < numCols; col++) {
      rowString += results.getString(col + 1) + '\t';
    }
    Logger.log(rowString);
  }

  results.close();
  stmt.close();

  let end = new Date();
  Logger.log('Time elapsed: %sms', end - start);
}

When running this code I get the following error:

Every time I run the code, I can see a new line in the mysqlerr logs:

I have the Cloud SQL instance set with the public IP, but I have not whitelisted any networks. The documentation does not mention it as a required step. Also I have set the project number for the GCP project of this Apps Script project, but still I get this error.

EDIT

As requested, I am adding more screenshots about the instance:

I am able to connect to the Cloud SQL instance using the gcloud sql instances connect command, and once inside I am able to query the table I want. (Bear in mind that the table is currently empty, as we are in the early stages of development at this point)

I believe this rules out the possibility of me using the wrong user/password.

As you can see I am using the default value for the max_allowed_packet flag. To be honest I have not set any flags on this instance yet.

About the connection name, I am using the format shared in the code snippet above, and actually I have copy and pasted it from the Cloud Console.

The next screenshot is the summary of the instance's settings:

Thanks in advance!