Purpose of this pull request

This pull request (PR) changes implementation of the GitHub Pages workflow to align with the native starter workflow and adds refactoring via reusable workflows.

This implementation introduces the following improvements:

• eliminates risks related to dependency on actions developed by individual contributors
• eliminates the need to maintain the gh-pages branch
• enables configuration options related to managing environments
• allows using the same workflow on the mainline, public forks, and private mirrors
• allows adding consistency with other projects
• reduces code duplication

Green run is here.