Cleanup common bootstrap shell code

What does this merge request do and why?

A follow up to !2859 (merged) to clean up shell code without distracting from the main logic.

How to set up and validate locally

1. Run ./support/bootstrap-packages on a clean system
2. Ensure log messages are informative
3. Package installation starts with no errors

Impacted categories

The following categories relate to this merge request:

• gdk-reliability - e.g. When a GDK action fails to complete.
• gdk-usability - e.g. Improvements or suggestions around how the GDK functions.
• gdk-performance - e.g. When a GDK action is slow or times out.

Merge request checklist

• This change is backward compatible. If not, please include steps to communicate to our users.
• Tests added for new functionality. If not, please raise an issue to follow-up.
• Documentation added/updated, if needed.
• gdk doctor test added, if needed.
• Add the ~highlight label if this MR should be included in the CHANGELOG.md.