GitLab.com links can appear in papers the same two ways GitHub links do: a real hyperlink, or a bare "owner/repo" mention near the word "gitlab". Only gitlab.com is matched; a self-hosted GitLab instance's own domain is indistinguishable from an arbitrary institutional website (see the file header comment).
Examples
paper <- demopaper()
gitlab_links(paper)
#> # A tibble: 0 × 3
#> # ℹ 3 variables: href <chr>, text_id <int>, paper_id <chr>