Replace interactions with GitHub to be run via gh cli in validate-n-build-api.yml

[ygrishajev]

Currently, our workflow uses curl commands to interact with GitHub's API. We should modernize this by using the official GitHub CLI (gh) which provides a more robust and maintainable way to interact with GitHub.

Purpose

Replace all curl commands and other possible interactions with equivalent GitHub CLI commands for better maintainability and reliability.

Grounds

• More readable and maintainable code
• Better error handling and authentication
• Native GitHub CLI features like automatic retries
• Consistent with modern GitHub practices

Implementation

Update .github/workflows/validate-n-build-api.yml:

1. Add GitHub CLI setup and authentication
2. Replace curl commands with equivalent gh commands
3. Update permissions if needed
4. Add proper error handling