If you want to keep everything inside a singular Nix configuration while still using Docker, you can check out the NixOS option virtualisation.oci-containers - essentially, a declarative way of managing docker/podman containers (similar to docker-compose) but with Nix.

when you copy/paste a file on your computer it’s much faster than copying the file

I think you meant ‘when you cut/paste a file’?

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.