You can bring your own Woodpecker CI or Forgejo Actions runners. The cheapest solution is to just run them at home in a VM.
Codeberg is a community driven project, which provides CI for FOSS projects, and it's a bit unfair to expect them to provide free compute for random and/or private projects.
For what it's worth, I've had better experience with running self-hosted Forgejo Actions runners compared to self-hosted Github Actions runners.
It exists yes, but you need to request access to it (which is manually reviewed), comes with a bunch of restrictions and it’s a limited resource.
I have several projects I’d want to move over but thats enough of a barrier for me to lose interest. There’s also Forgejo Actions but I assume paying for your own runner is probably more expensive than GitHub.