Use GitHub Action for deployment.

[XAMPPRocky]

This allows using the repo's GITHUB_TOKEN and will only push when there's actual changes.

[rust-highfive]

r? @nikomatsakis

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[pietroalbini]

r? @pietroalbini

This mostly looks fine. While reviewing the PR, I noticed both the new and the old versions don't create a .nojekyll file at the root of the deployed website, while that file should be created to avoid extra preprocessing by GitHub.

Could you add that? A simple touch site/.nojekyll should be enough.

[XAMPPRocky]

@pietroalbini Done.

[pietroalbini]

Thanks!