He is likely referring to the CI runners. Gitea has their own version of Actions runner. It is very much usable, though currently inferior to GitHub Actions (not always a 1:1 replacement, even though they aim for it to be): https://docs.gitea.com/usage/actions/
Cost as always depends on your usage, but it will likely be less than your current cost of GitHub Actions.
Thank you. This is exactly what I meant. I work for a large company where our testing budget is massive and most of it goes towards these CI runners. Provisioning enough and consistent compute for testing pipelines sometimes becomes the bane of my existence.