Hi vincentaudeval,
Thank you for your purchase.

Sorry for late response, we are not working on weekends.

In some cases, the hosting provider doesn't allow any other SMTP (like gmail) other than their own, but if you contacted the provider, and they say it looks good, then this is not that case.

We have had some issues with gmail set-up, and the workaround you used (installing WP Mail, and entering the gmail credentials) is actually what we are suggesting other users when this issue comes up. We haven't yet been able to exactly pin point why it happens for some customers, while others use it normally, but our team is involved in resolving this issue for one of the future releases.

Until then, you can keep using the WP mail plugin, and it should work fine.

Best regards.