Hi,
In our cases, we use AWS Lambda for webhook event scripting as it’s written in the official document.
For instance, in AWS, you can setup AWS Lambda with API Gateway to create webhook apps (or even you can use AWS SAM to encode those application buildings).
API Gateway provides actual endpoint that you’ll put into the Shotgun wehbook’s url attribute and that triggers AWS Lambda function which executes scripts you want.
The image below is an exmaple flow to contact with Shotgun to get Shotgun info and sending notification to Slack.

The basic ideas are almost same, even if you use other services I think.
So I hope that will help you.