I self-hosted Pushin on my own Forgejo instance on a Hetzner bare metal server before Pushin was ready and it was a great experience to be honest! Self-hosting Forgejo is great!
Is your code safe on hetzner though? I wanted to do something similar but I'm hesitant about what hetzner employees can see on the machines so I don't know how private and safe it would be to store code there.