Multiple forks on GitHub

I tried to make a second fork of the same third party project on github using the following instructions:
https://adrianshort.org/create-multiple-forks-of-a-github-repo/
Unfortunately github does not allow me to create a pull request up downstream for such a "fork" - there is no such button and upstream branch in the dropdown. It doesn't seem to think it's a fork at all - the project icon is different.
Obviously the changes I made locally with git remote add upstream

are ignored by the github server.

Any way to fix this?

I want two fully functional (PRs should have worked) forks of the same project under the same github user account.