There are any number of email sending providers with API access - Sendgrid, Mailgun, Mailjet, etc. Amazon SES is the most cost effective, but you'd need to do more setup youself vs. one of the API senders.
There are also some best practices to keep in mind when sending system emails like this, like not using that same system for marketing emails since they're more likely to get flagged as spam.
Easily worth the added benefits of the API