Github App to be used across Multiple GHEC Instances

### Is your feature request related to a problem?

We want to use this App across multiple GHEC Instances . So Public Mirrors in GHEC Instance 1 & Private Mirrors in GHEC instance 2 because our GHEC 2 is not allowed to have Public Orgs. Is there a way to accomplish this ?

### Describe the solution you'd like

Want to have this Github App working across multiple GHEC Instances as we have separate GHEC instances for Public and Private Forks

### Describe alternatives you've considered

_No response_

### Additional context

_No response_

No files, tests, or entry points are identified in the issue. Start by reviewing how the GitHub App configures authentication and selects a GHEC instance, then define the instance boundaries and permissions needed for public and private mirrors; done means one App can support both GHEC instances without violating their organization restrictions.

Written by the indexing model from the issue text.