In the preface to the 1882 Russian edition of the Manifesto, Marx and Engels say that the Russian commune could “pass directly to the higher form of Communist common ownership” only if the Russian Revolution (which he saw as inevitable, though it was not inevitable that it would "take[] place in time" (first draft of letter to Zasulich), and in the Letter to Otecestvenniye Zapisky he says that if Russia continues on its path, it will have lost this chance to skip the phase of capitalist development) is supported by wider revolution in the West. Otherwise, the Russian commune “must [] first pass through the same process of dissolution such as constitutes the historical evolution of the West.”

There’s zero approval by Marx here for the notion of skipping the phase of private production/property in one country without a wider revolution.

Marx told Zasulich at the time that education was one of the most crucial factors in the possibility of bypassing the agonizing stage of capitalism.

No he didn’t.

You misinterpret Marx's statement. I'm fully aware of Marx's views on the Russian commune movement, the problem is that you assume the Soviet model is what Marx was referring to, and that a more classically Marxist understanding of socialism was not what he meant. Marx was fairly explicit in what a socialist state would be, one where public ownership is principal and the working classes control the state. The Russian peasantry could have bypassed the dictatorship of the bourgeoisie and went straight to a dictatorship of the proletariat and peasantry, but they would not be able to avoid the problem of transitioning small ownership to large, industrialized ownership without the aid of markets.

The fact of the matter is that private property existed de facto in the USSR. One of the mistakes of former socialism was merely trying to punish private ownership, rather than subordinate it to the public sector. Marx analyzed markets as being enormously useful in stitching together all of the small owners and building up productive forces, and public ownership as being superior at running large industry.

Stalin ending the NEP early was a matter of survival, and was correct. China's conditions are different, and now occupies a more classically Marxist economy. It isn't even the same as the NEP, China was closer to the NEP under Mao, the socialist market economy of China is a more classically Marxist economy, with the ability to be so precisely because the imperialists cannot afford to decouple from them.