Well, FluentSMTP is a plugin that integrates your WordPress site with an outgoing email service such as AmazonSES. And, I do use that and it works well. 🙂 However, I don’t think that’s what you’re referring to.
When I stopped using Gmail for all my email, I migrated to FastMail. And I manage all my domain-based emails (actually all email) from FastMail.
But, that’s different than outgoing email from your server, which is what FluentSMTP does.