The Move repository button located at the upper right inside a Repository Details page can be hit do move a repository to another project.

However, after moving a repo to another project, It is still possible to clone the repo using the old URL.

This behavior will work forever. To get rid of the redirect, it's necessary to create a new blank repository as the same name of the old repository in the old project, and then delete this repository. This action should clear out the redirect.

I've performed this test on my instance and it will be possible to create a new empty repo in the original project using the same repo's name as previously. If you perform a clone pointing to the new URL, it will pick up the new reference (an empty repo.)

I'm raising this to add this information to the documentation since we got this feedback from a customer.