[FEAT]: Rename GITHUB_APP_PEM_FILE to GITHUB_APP_PRIVATE_KEY for consistency with GitHub terminology

[jamesgeddes]

Describe the need

On the GitHub App configuration page (https://github.com/organizations/[owner]/settings/apps/[app name]) and throughout GitHub’s official documentation, the .pem file that a GitHub app provides is referred to as a "private key". The GitHub Terraform provider, however, currently uses the variable name GITHUB_APP_PEM_FILE instead of GITHUB_APP_PRIVATE_KEY.

While functionally equivalent, this inconsistency makes knowledge transfer more difficult because:

1. Users must manually confirm that GITHUB_APP_PEM_FILE refers to the private key rather than another GitHub App credential.
2. Other GitHub tools, such as GitHub Actions (actions/create-github-app-token), use private-key, leading to unnecessary confusion.
3. Using GitHub’s native terminology improves clarity and reduces onboarding friction.

Proposal

• Introduce GITHUB_APP_PRIVATE_KEY as the preferred variable name.
• Continue supporting GITHUB_APP_PEM_FILE as a deprecated alias for backward compatibility.

This change would ensure consistency across GitHub’s ecosystem while maintaining existing behavior for current users.

Could this improvement be considered?

SDK Version

No response

API Version

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Relevant log output

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