git fetch --all
This means "fetch from all remotes". How many remotes do you have? What are their URLs? (Use git remote -v to list them.)
I get the error message:
fatal: '/html/project' does not appear to be a git repository
Could not read from remote repository.
Please ensure that the correct access permissions exist and the repository exists.
This means that at least one of your remotes—we won't know which one(s) until you run git remote -v to list them—has /html/project as its (Git-extended-style) URL. Or—here's the tricky bit—perhaps one of them has ssh://<ssh-part>/html/project.
So I logged in via ssh to my server ...
That's fine, but it misses out on the tricky part.
... and [/html/project on that computer is a Git repository]
It sounds like your URL should be ssh://your.server.full.dns.name.goes.here//html/project or similar, rather than just /html/project. (Whether you need a user name here depends on how your ssh login to this server works.)
Note the double slash!
You mention in comments that the URL is:
ssh://myuser@myhost.de:2222/html/sulu
(for both fetch and push), and that's the problem. Even with the ssh://myuser@myhost.de:2222 part, which directs your Git to (in effect) use ssh -p 2222 myuser@myhost.de to get to the remote, the URL your Git provides to myuser@myhost.de is not /html/sulu but rather html/sulu.
Git isn't really aware of all of this—it doesn't do a lot of fancy parsing work—so Git thinks it's presenting /html/sulu, but it isn't. It's presenting html/sulu.
When ssh connects to another machine, you start out with your current working directory being your home directory. For instance, my home directory is /home/torek (Linux) or /Users/torek (macOS). So any relative URL, as for:
ssh://my.host.name/src/proj
refers to /home/torek/src/proj or /Users/torek/src/proj. But you want /html/sulu, something not in your home directory.
You can typically get there by using the double slash trick: ssh://myuser@myhost.de:2222//html/sulu. The ssh code strips off one slash, leaving /html/sulu as the path, which then works.
Sometimes the ssh system doesn't let you do this—it's all up to ssh; none of it is up to Git—and in that case you may need to use some other trick, such as making a symbolic link in your home directory on the server.
