### Check for existing issues

- [x] I have searched the existing issues and checked that my issue is not a duplicate.

### The Feature

LiteLLM should support adding Claude skills (and similar AI skill plugin integrations) to private repositories. There should be a supported way to authenticate to a private repo, either via SSH key or a GitHub access token, so that skills can be used with code in private codebases. Currently, there is no clear documentation or programmatic support that covers how to authenticate and enable skills for private repos (local or GitHub-based) using the skills API.

Feature Scope: - Allow registering or attaching Claude skills to private repositories - Support passing authentication, via either: - SSH private key for custom repos - GitHub access token for directly accessing private GitHub repos - Surface clear authentication errors and provide documentation for configuration - Expose this as part of the `add_skill` and store authentication info approproately - Provide inputs for auth in proxy UI

If this is already possible, add documentation and a reference workflow for secure setup.

### Motivation, pitch

Many organizations and developers use pri…