google/go-github ? reverse-engineered prompt

Build me a Go library for talking to the GitHub REST API v3.

I want it to feel like a clean client that lets me create a GitHub API client, authenticate with a personal access token or a custom HTTP transport, and then call grouped services like organizations, repositories, issues, pull requests, and other common GitHub endpoints in a simple way. Please include a few clear examples showing how to list orgs and repositories, and how to pass a context and optional parameters.

It should support both regular OAuth token style auth and GitHub App style auth through a transport or HTTP client, and it should be easy to extend with more endpoints over time. If there are existing docs or API references that help, look them up online if needed. Also make sure the code is idiomatic Go, works in module mode, and includes enough tests and sample usage so someone can actually use it right away.