The gulf countries are the closest thing to socialist states on the planet. Something like 70-90% of the citizenry of Kuwait, Qatar, and Saudi Arabia are employed by the public sector.
That's not socialism. It's an absolute autocratic monarchy distributing oil rents to a privileged citizen caste.
Most of the private-sector work is done by foreign workers who don't receive the same benefits or political rights.
State ownership alone isn't sufficient. If a hereditary ruling family controls the state, then "state ownership" just means ownership by that ruling elite, not by society.