Then I am able to continuously read new emails, read the info on a server, process the info make API calls then generate an accurate response and send the appropriate response.
Any help with an appropriate stack and technologies would be greatly appreciated.
https://serverfault.com/questions/506894/how-to-route-email-...
In that case you'd need to run a mail server where you install a script. I've done it with qmail and postfix but I haven't run my own mail server for a long time.
Another option is to use an existing mail server but write a script that polls the mail server with POP or IMAP.
Today I'd consider doing it serverless with something like
https://aws.amazon.com/about-aws/whats-new/2019/02/trigger-a...
So far as the "stack" I would go with any mainstream platform, mostly driven by what you like. You could certainly do this with Python, Java, .NET, etc.
You can totally do exactly what OP wants. Use the inbound parse webhook, get mail forwarded to your HTTP webhook/endpoint, do whatever you want, and then you can even reply using the email API of the provider. No reason to sweat the mail server stuff.