GitHub app based authentication

### Describe the Feature

Most organizations prefer to use the GitHub app instead of a user token for authentication as the token has an API limit of 5000 whereas the GitHub app goes all the way to 12500.

### Expected Behavior

https://docs.github.com/en/apps/creating-github-apps/authenticating-with-a-github-app/about-authentication-with-a-github-app

### Use Case

We reach the API limit on our application on a daily basis.

### Describe Ideal Solution

https://docs.github.com/en/apps/creating-github-apps/authenticating-with-a-github-app/about-authentication-with-a-github-app

### Alternatives Considered

_No response_

### Additional Context

_No response_

Start by reading the linked GitHub App authentication documentation and locating the repository's existing user-token authentication entry point. Determine how GitHub App credentials and installation authentication should fit the CLI; done means organizations can use GitHub App authentication to access the higher API limit.

Written by the indexing model from the issue text.