I built something on those lines, although way simpler in terms of functionalities and resources used.

All I wanted was to receive/send emails from a custom address (@acme.com) using Gmail, but I didn't want to pay Google Suite for that.

So I used SES+S3+Lambda to receive emails and forward then to a Gmail alias (email+acme@gmail.com) so I can attach a filter on them using a label. And for sending emails using the address, I simply authenticated it on Gmail using the "Send mail as" option using AWS SES SMTP credentials.