Hi,
I would love to help you implement this feature.
I have lots of experience working with Git (including GitLab) and deploying websites. I also have experience with Git Hooks, which is the mechanism by which you can perform actions when code is committed to a git repository. In your case this would be deploying your site to the test/production server.
I know that you are not just interested in receiving a solution, but that you wish to understand how it works to. If I am successful with the bid you will receive full documentation on what work has been completed and how it works, and I would be happy to answer any questions you may have.
I would be able to complete the task in about 1 day. I am UK based.
Thanks,
Joe