This commit migrates this functionality away from the bots. Nowadays
it's possible to build and deploy the website to GitHub Pages directly
through the GitHub Actions, which provides a nice simplication of the
process. Not only does this remove the requirement to have a `gh-pages`
branch in the repository, it also avoids the complexity of having to
configure the workflow to commit to Git branches and allows us to remove
the Git committing code from the Gulpfile.
Note that deploying directly though GitHub Actions workflows needs to be
enabled in the repository settings, but this is easy and well documented
on the link below.
The following resources are relevant for this patch:
- Enabling deployment to GitHub Pages directly through GitHub Actions:
https://docs.github.com/en/pages/getting-started-with-github-pages/configuring-a-publishing-source-for-your-github-pages-site#publishing-with-a-custom-github-actions-workflow
- Uploading GitHub Pages artifacts example:
https://github.com/actions/upload-pages-artifact#usage
- Deploying GitHub Pages artifacts example:
https://github.com/actions/deploy-pages#usage
