Register Library on Gitlab

There is no need to do that. Simply create a free GitHub account and then submit a pull request to add the URL of the GitLab repository of the library to the repositories.txt file in the arduino/library-registry repository on GitHub. It will take a matter of minutes to complete the simple task and then you can forget all about GitHub after that if you like. You can even delete your GitHub account after that if you don't think you will ever want to use GitHub again.

Please note that there is no need for you to switch to using GitHub for hosting your own projects, including Arduino libraries. You are welcome to continue to use GitLab for that. It is only necessary to use GitHub when you want to contribute to repositories like arduino/library-registry that are hosted on GitHub.

I recommend you just give it a try. I think things will become more clear to you once you do it.