China

in addition to the excellent China Has Billionaires which Yogthos already linked you, read this explanation as well

What makes a country "socialist"?

A society where public ownership of the means of production, a state controlled by a politically organized proletariat, and production for societal use rather than for profit is the principal aspect (main body) of the economy.

Key term here is principal aspect. There is a weird phenomenon from both anti-communists as well as a lot of ultraleft and leftcom communists themselves of applying a "one drop rule" to socialism, where socialism is only socialism if it's absolutely pure without a single internal contradiction. But no society in the history of humankind has been pure, they all contain internal contradictions and internal contradictions are necessary for one form of society to develop into the next.

If you applied that same logic to capitalism, then if there was any economic planning or public ownership, then capitalism would cease to be "true capitalism" and become "actually socialism", which is an argument a lot of right-wing libertarians unironically make. The whole "not true capitalism" and "not true socialism" arguments are two sides of the same coin, that is, people weirdly applying an absolute purity standard to a particular economic system which is fundamentally impossible to exist in reality, so they then can declare their preferred system "has never truly been tried". But it will never be tried ever because it's an idealized form which cannot exist in concrete reality, actually-existing capitalism and socialism will always have internal contradictions within itself.

If no idealized form exists and all things contain internal contradictions within themselves, then the only way to define them in a consistent way is not to define them in terms of perfectly and purely matching up to that idealized form, but that description merely becoming the principal aspect in a society filled with other forms and internal contradictions within itself.

A capitalist society introducing some economic planning and public ownership doesn't make it socialist because the principal aspect is still bourgeois rule and production for profit. This would mean the state and institutions carrying out the economic planning would be most influenced by the bourgeoisie and not by the working class, i.e. they would still behave somewhat privately, the "public ownership" would really be bourgeois ownership and the economic planning would be for the benefit of the bourgeoisie first and foremost.

A similar story in a socialist society with markets and private ownership. If you have a society dominated by public ownership and someone decides to open a shop, where do they get the land, the raw materials, permission for that shop, etc? If they get everything from the public sector, then they exist purely by the explicit approval by the public sector, they don't have real autonomy. The business may be internally run privately but would be forced to fit into the public plan due to everything around them demanding it for their survival.

Whatever is the dominant aspect of society will shape the subordinated forms. You have to understand societies as all containing internal contradictions and seeking for what is the dominant form in that society that shapes subordinated forms, rather than through an abstract and impossible to realize idealized version of "true socialism".

Countries like Norway may have things that seemingly contradict capitalism like large social safety nets for workers funded by large amounts of public ownership, but these came as concessions due to the proximity of Nordic countries to the USSR which pressured the bourgeoisie to make concessions with the working class. However, the working class and public ownership and economic planning never became the principal aspect of Norway. The bourgeoisie still remains in control, arguably with a weaker position, but they are still by principal aspect, and in many Nordic countries ever since the dissolution of the USSR, the bourgeoisie has been using that dominant position to roll back concessions.

The argument for China being socialist is not that China has fully achieved some pure, idealized form of socialism, but that China is a DOTP (dictatorship of the proletariat) where public ownership alongside the CPC's Five-Year plans remain the principal aspect of the economy and other economic organization is a subordinated form.

—zhenli真理