in order to work with ssh cloning, one has to manually install openssh-client to the docker image, looks like that

Correct, you have to have SSH inside the container so that git can use it.
You can always install with the following setup inside your agent's clearml.conf:
extra_docker_shell_script: ["apt-get install -y openssh-client", ]
https://github.com/allegroai/clearml-agent/blob/73625bf00fc7b4506554c1df9abd393b49b2a8ed/docs/clearml.conf#L145