Gitea isn't meant to replace Github... it's meant to be a self-hosted alternative to it. That's subtly different.

I use it for as my local git server on Debian 9. Binary is in the /home/me/gitea directory. Run the usual gitea setup, then copy this to /home/me/.config/systemd/user/gitea.service:

  [Unit]
  Description=Gitea (Git with a cup of tea)
  After=syslog.target
  After=network.target

  [Service]
  RestartSec=2s
  Type=simple
  WorkingDirectory=/home/me/gitea
  ExecStart=/home/me/gitea/gitea web
  Restart=always

  [Install]
  WantedBy=default.target

Then just systemctl --user daemon-reload && systemctl --user enable gitea. Then visit localhost:3000 and add it to your remotes (git remote add local ...) and you can push your changes to your own gitea instance.