1. Issue the following git command git worktree add --checkout ../gh-pages gh-pages in the git root
2. dotnet build to build the dll for the metadata extraction.
3. docfx metadata to generate the latest metadata.
4. docfx build to build the site into the gh-pages worktree location.
5. docfx --serve to serve the site from the gh-pages worktree location.
6. If it all looks good, navigate the console to ../gh-pages and commit/push the site updates.

I had to modify the metadata section of the docfx.json file from:

{
  "metadata": [
    {
      "src": [
        {
          "files": [
            "src/**.csproj"
          ],
          "src": "../"
        }
      ],
      "dest": "api",
      "disableGitFeatures": false
    }
  ],
  // ..
}

to

{
  "metadata": [
    {
      "src": [
        {
          "files": [
            "OpenGraphNet.dll"
          ],
          "src": "../src/OpenGraphNet/bin/Debug/net6.0"
        }
      ],
      "dest": "api",
      "disableGitFeatures": false
    }
  ],
  // ...
}