Gitea supports migrating from a variety of sources, but I'm not sure about a bot that does everything in one click or so. You could probably make a simple script for that, though.
Gitlab does have it. @Darken@reddthat.com you can provide a personal access token to Gitlab and it'll import your repos with all the issues and pull requests intact.
I've migrated all my repos (not much, around 50 repos or so) to GitLab this January, GitLab has a built-in tool for that, it was as easy as a single click once I authenticated GitHub to allow that.