IF you really don't want to download a repository, you might consider using a GitHub Action.
It does access your code on GitHub side, and can execute whatever you need.
A GitHub Action has an API, and use GitHub runner (on GitHub side, so no download on your part) as opposed to self-hosted runner.
A workflow can be anything you need, like for instance github-action-build
, to build your project, in a repository-specific fashion.
As an example, github-action-for-latex
compile Latex documents, using a Docker image (xu-cheng/latex-docker).
You would need a similar approach, using a Docker image where you can clone that repository, and execute it (because the Docker image would have everything needed to run your project).
And that would be done entirely on GitHub (Azure-based) side.