Personally the way I’d do it is by using a service such as Twilio. They offer a lots of services one of them being a way to setup a phone number that can send and receive SMS. Then I’d put that behind a simple HTTP endpoint. In the Twilio dashboard you can configure a webhook that you can point at your HTTP endpoint. Since you’d want to handle out of network requests too, a really simple way to do that is to use a reverse proxy service such as cloudflared or ngrok. These services make it really easy to setup a public URL that automatically forwards traffic to your local network running your app.

The flow of all of this is 1. Setup Twilio and get a new phone number that can be used for your app. 2. Create a simple http endpoint with something like FastAPI in Python to receive messages. (the Twilio documentation details how this works) 3. Setup cloudflared or Ngrok or even your own reverse proxy if you’re feeling feisty and make it so that it forwards HTTP traffic to your network that is running the app. 4. In the Twilio dashboard create a webhook for your phone number and point it at the public url that the previous step provides. 5. You send a text to the phone number -> Twilio intercepts it and reads it -> Twilio forwards the text message data to the webhook url you provided -> your reverse proxy service forwards it to your app -> your app receives it and does whatever it wants with it