RROR: ER_NOT_SUPPORTED_AUTH_MODE: O cliente não suporta o protocolo de autenticação solicitado pelo servidor; Considere atualizar o cliente MySQL
Execute the following query in MYSQL Workbench
ALTER USER 'root'@'localhost' IDENTIFIED WITH mysql_native_password BY 'password';
Where root as your user localhost as your URL and password as your password
Then run this query to refresh privileges:
flush privileges;
Try connecting using node after you do so.
If that doesn't work, try it without @'localhost' part.
guruwalker