Fix the Review App `base-config.yml` change detection

What does this MR do?

This fixes the base_config_changed function to properly detect when the base-config.yml file is modified by fetching the API instead of relying on git.

Does this MR meet the acceptance criteria?

Conformity

• Code review guidelines
• Merge request performance guidelines
• Style guides
• Separation of EE specific content

Availability and Testing

A working example can be seen at https://gitlab.com/gitlab-org/gitlab/-/jobs/343655761.