Place your extension source into src dir in the root of the git repository.

Create a new workflow by going into the "Actions" tab.

workflow "New workflow" {
  on = "push"
  resolves = ["App Inventor Extension"]
}

action "App Inventor Extension" {
  uses = "pavi2410/AIX-Action@master"
}

Now, whenever you push a commit, the extension will be built automatically and can be located at $GITHUB_WORKSPACE/appinventor-sources/appinventor/components/build/extensions