You may want to try cloning your upstream repo with --mirror option and then push to your new remote with --mirror option too
You’ll have the following flow:
git clone <upstream-repo-url/repo.git> --mirror
cd <repo>
git remote add <your-remote-name> <your-remote-url/repo.git>
git push <your-remote-name> --mirror
⚠ Be really careful with the push --mirror as it will delete branches that are on your <your-remote-name>