Add private repo sync

[billytrend-cohere]

This PR introduces a new workflow named private-repo-sync to the .github/workflows/sync-private-repo.yml file. The workflow is triggered on a push event and is designed to synchronise a private repository with a public one.

Changes:

• A new workflow named private-repo-sync is added.
• The workflow is triggered on a push event.
• The workflow runs on the ubuntu-latest runner.
• The workflow uses the actions/checkout@11bd71901bbe5b1630ceea73d27597364c9af683 action to checkout the repository.
• The workflow uses the actions/create-github-app-token@5d869da34e18e7287c1daad50e0b8ea0f506ce69 action to create a GitHub app token.
• The workflow adds a private remote repository using the generated token and pushes the current branch to the private repository.

[github-actions]

🌿 Preview your docs: https://cohere-preview-923e7bee-7e19-48f5-a12f-d0d1932e956a.docs.buildwithfern.com