UPD: The issue with missing cmk-agent user does not reproduce with the latest checkmk/check-mk-raw:2022.09.15 docker image.
However, the socket issue is still there (/run/check-mk-agent.socket is missing). As a workaround, I tried to create symlink, and it seems to work fine:
ln -s /var/lib/cmk-agent/scripts/super-server/0_systemd/check-mk-agent.socket /run/check-mk-agent.socket