The really simple setup for a single user is just a SSH server with access to storage and the git command. Assuming your laptop and desktop have SSH access to server, you can just:

ssh server git init --bare somerepo
cd somerepo
git remote add server server:somerepo
git push --set-upstream somerepo master #(or main)

and then git clone server:somerepo.

For something slightly higher-tech, I recommend going with Forgejo (the fork of Gitea). It is really easy to set up and low maintainance.

Avoid GitLab for small setups, it is fairly resource hungry.

I have a private instance of Forgejo in docker on my server. took me all of 5 minutes to set up. I did this only because I wanted a web based GUI for some stuff.

Many excellent replies. Just want to add https://github.com/charmbracelet/soft-serve as an option

SSH is all you need. You can clone directly from one .git directory to another.

e.g

git remote add desktop git@desktop:project/.git
git push desktop main --set-upstream

git init --bare

And then just ssh to the server to push/pull. It can’t be any simpler

Check out Gitea. It was pretty easy to set up with docker and they have pretty decent docs.

The simplest (really the simplest) would be to do a git init --bare in a directory on one machine, and that way you can clone, push or pull from it, with the directory path as URL from the same machine and using ssh from the other (you could do this bare repo inside a container but really would be complicating it), you would have to init a new bare repo per project in a new directory.

If a self-hosted server meaning something with a web UI to handle multiple repositories with pull requests, issues, etc. like your own local Github/Gitlab. The answer is forgejo (this link has the instructions to deploy with docker), and if you want to see how that looks like there is an online public instance called codeberg where the forgejo code is hosted, alongside other projects.

If you fancy a nice webbased interface, Forgejo. Git bare with cgit is an option of course, but running the single application for Forgejo will you lots of fun.

This is not the simplest answer at all but FYI you can also self host gitlab

I’ve played with Gitea a little and it was easy to set up, but I didn’t need the web stuff. So as others have suggested, I just set up a bare git repo in one place, then git clone it over ssh in the other place, and push and pull to it. So that’s an SVN-like model with a central repo, plus a few other places using it and sometimes pushing code to it that I manually pull when needed to the others.

All this stuff with docker containers seems like ridiculous overkill.

Using git is oftentimes a good idea but does not fit your description. Just use syncthing or another cloud thing. You can still use git but without a dedicated berg/tea/hub/lab/bucket server