Now in 2024 we can publish GitLab-pages in another folder than public.

To do so, in your .gitlab-ci.yml add : publish: dist

A short but working example :

pages:
  script:
    - ls
  artifacts:
    paths:
      - dist
  publish: dist

For more, I found the publish syntax there.

And if you prefer, there are some workaround explained in the official documentation.