I was confused about the name and owner fields because the documentation does not fully explain that if you are using an org, then name should be the org name which was my issue here.

publishers: [
    {
      name: '@electron-forge/publisher-github',
      config: {
        repository: {
          owner: 'MyOrg',
          name: 'my-repo'
        },
        prerelease: false,
        draft: true
      }
    }
  ]