Well, yes, they are clearly separate companies. But they both utilize git. The git process for making a copy of a repository, making a branch, and requesting for the changes in your branch to be added to the main branch, are the same.
The issue is that the UI process for doing this differs between the two companies web interface.
library-registry/repositories.txt at main · arduino/library-registry · GitHub
This clearly shows Gitlab hosted libraries added to the library manager, so it's definitely possible to do, it just seems very roundabout for you to have to create a Github account, just to add your Gitlab repo URL to the file.
There is some information on stack exchange about setting a Github repo as the upstream for a Gitlab repo but these seems to be more about porting a repository over rather than having a Github repo merge changes made in a Gitlab repo.