Corporations are constructs of the state.
Yes, but so are people, nowadays. You try getting anywhere in life without an official piece of paper proving who you are and what state you're affiliated with.
Socialism is a power structure that depends on the state to support it. Taxation required and the forced confiscation of earnings of the workers needed to keep it functioning is the same power tyrants use. There is no difference. Socialism is a form of Statism. Your view that Socialism has no attachment to a state is simply incorrect, as it requires a state to tax the workers (forcibly take) in order to give to those that it chooses to support. Unless you can name a Socialist system that doesn't contain confiscatory taxation policy, your point is simply wrong.
I can't name one which has actually operated in modern times, but there have been such systems in the distant past, and there are advocates for such systems in the future. The "socialism" advocated by Marx and Engels (a term they used interchangeably with "communism") was to be a world in which money and states had been abolished; without these there would be no "confiscatory taxation", but rather a contribution and distribution of wealth according to individual abilities and needs. When you say that "socialism is a form of statism", you are probably attacking ideologies such as Leninism and its variants (and maybe also much "softer" systems such as so-called "democratic socialism" popular in Western Europe). Lenin also nominally believed in socialism and communism (in the Marxian senses of the words) as an end-goal, but held that the only way of reaching this goal was for the state to first take control and build up the capitalist economy. He called this "state capitalism", and eventually redefined the term "socialism" to be synonymous with it. Seventy years after his revolutionaries seized power, the Russian people were still living under state capitalism with no real socialism in sight.