Replace start-task and post-update-task with own duration collector

What does this merge request do and why?

This MR replaces start-task and post-update-task in the update rake task with our own duration collector.

This is in preparation to turn rake update into a spinner_task in !3902 (merged), so we can still show the duration.

Screenshots

Before	After

How to set up and validate locally

1. Run GDK_SELF_UPDATE=0 gdk update
2. See the new duration status

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.
• Announcement added, if change is notable.
• gdk doctor test added, if needed.
• Add the ~highlight label if this MR should be included in the CHANGELOG.md.