I followed the guide here https://docs.github.com/en/free-pro-team@latest/actions/learn-github-actions/sharing-workflows-with-your-organization.
I successfully created a GitHub Organization shared workflow and can access this shared workflow if I create a public repo under the organization or my account (I am a member of the organization).
However, if I create a private repo I do not see the shared workflow. I am using the free-tier for my membership account and organization, so I'm not sure if that is the issue. There was no documentation stating that was a requirement.
Only possible in GitHub Enterprise plan organizations:
to use templates to create workflows in private repositories, the organization must be part of an enterprise plan. GitHub documentation