docs: more in-depth private package documentation

[jamietanna]

Describe the proposed change(s).

• cross-org GitHub access when using a GitHub App or Fine Grained Personal Access Token

Potentially some of these suggestions from Claude:

  ### Private registries — the most painful area

  "Support Private Authentication in Package Rules" has 45 upvotes (the most of any discussion). "GitHub Private Repos - Cross Org Stopped Working" has 43 upvotes. The  private-packages.md  doc exists but apparently doesn't cover enough sc
enarios.

  The common private registry questions in discussions:

  • Private PyPI with pip-compile/uv
  • Yarn v2  npmAuthToken
  • Docker Hub rate limiting and authenticated pulls
  • Private GitHub registries cross-org
  • Artifactory multi-registry setups

  Each of these is a distinct setup that needs its own example. The current  private-packages.md  is likely too general.