Fixing the doc publishing build

[john-science]

What is the change?

I update the version of the tool we use to publish our ARMI docs.

Why is the change being made?

The version of the doc publishing tool we were using (JamesIves/github-pages-deploy-action) went out of date, and suddenly just broke on us. I had to update it to get it working again. (The version we were using was from August 2021, so I suppose that's the lifetime of such GitHub Actions tools.)

Proof this Change Works

As proof this change works, please see this test commit I ran: https://github.com/terrapower/armi/actions/runs/9165270178

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Checklist

• [X] This PR has only one purpose or idea.
• [X] Tests have been added/updated to verify any new/changed code.

• [X] The code style follows good practices.
• [X] The commit message(s) follow good practices.

• [X] The release notes have been updated if necessary.
• [X] The documentation is still up-to-date in the doc folder.
• [X] The dependencies are still up-to-date in pyproject.toml.