I don't think that prompt alone would send your form data to your email. We're using Nodemailer under the hood, while you could "prompt engineer" your way to having functional forms, configuring things like custom SMTP would take more than just that prompt. The idea with Formbee is to have a fairly low friction way to send form data to email, or webhooks. With the hosted option its as simple as sending a post request, self hosting can be as easy as spinning up a docker image, and configuring a few env vars.
Lambda is great though! We should add some Lambda boilerplate to our docs to make it easy to self host form submission with Lambda.