Trade and wage labor also aren’t exclusive to capitalism.

Yes, trade isn’t exclusive to capitalism, I never claimed otherwise. However, there is a distinction between commodity exchange for exchange-value (capitalist trade) and international distribution of goods to satisfy needs (socialist distribution), whether through planned allocation or transitional forms like labor vouchers.

Wage labor is specific to capitalism, it’s a sale of labor-power as a commodity, exchanged for a wage, with surplus value being appropriated by a class/managerial apparatus. This is THE fundamental relation of capitalism, and you’d be better off reading theory than blindly quoting it.

Though I will give a concession - socialism is such a meaningless term that it means like 4 different things depending on who says it: liberals would say it’s social democracy, ML’s say its state capitalism, Marxists and Leninists say it’s socialist mode of production (post-transition period) and Posadists would say it’s when nuclear annihilation. A word doesn’t make a thing so if you consider state capitalism to be socialist - fair, all power to you. However - Marxists, Leninists, Liberals would all collectively disagree. You did drop a Lenin quote to strengthen your argument so let me do the same:

• Lenin, The Tax in Kind

No one, I think, in studying the question of the economic system of Russia, has denied its transitional character. Nor, I think, has any Communist denied that the term Soviet Socialist Republic implies the determination of the Soviet power to achieve the transition to socialism, and not that the existing economic system is recognised as a socialist order.

In the same text he also calls NEP USSR as state capitalist due to the concessions he had to make for the transition, which is explicitly made distinct from Socialism.