I have found that the easiest way to play around with or test extensions code running on the server is to create a command that triggers a server event. This repo contains several commands that demonstrate the logging capabilities of backend server events.
If you want to test some arbitrary code, just drop it in one of the existing events or create a new one with a command trigger of your own.
To run a command after installing the extension, open the search dialogue in Aha! - magnifying glass in the top right corner - and click on the "commands" tab. You can also get there via hotkeys by pressing "/" to open the search modal and then ">" to navigate to the commands tab.
See https://www.aha.io/support/develop/develop/extensions/extensions-introduction for documentation on extensions and their installation process.