Classes like the Party members, the Bureaucracy members, the Military members does not make for a classless society, and neither does the work hierarchy and the use of Taylorism and Fordism.
More importantly to the current times, "surplus" based on cheapened nature such as undervalued waste sinks may not actually be a surplus, but a loss.
the change to capitalism didn‘t improve that.
The change from State Capitalism to Private Capitalism, indeed, did not improve that.
It doesn't make a classless society, but it is necessary at least for a short while to establish the class rule and an actual path towards socialism and withering away of the state.
You can't have socialism without having all of people's needs met which requires repurposing the means of production, you can't have socialism without strong control during the post-revolutionary period given the counter-revolutionary tendencies of bourgeoisie/third-party opportunistic groups (most revolutions happen in pairs/chains, its the most volatile period) - that's the purpose of the period of transition.
Historically, countries such as USSR, China (though its a question if China's revolution was proletarian at all) and later didn't get past the transitionary period because of tens if not hundreds of millions of peasantoids and underdeveloped industry, having them to stay in this awkward period for a long time, which led to complete degeneration of ideology after opportunists took the reigns (like Stalin), who bastardized the meaning of Socialism and essentially caused the countries to become "red bourgeois".
Nope, it still is exploitative, given how surplus value implies workers not being paid full value for their labor. Even if workers were to seize the means of their production and got a say over their surplus value and where it gets repurposed, it'd still be exploitative due to how markers and competition works, and workers having to exploit themselves by "paying themselves" less, as that's the only area where you can reliably cut costs of production.
The only non-exploitative mode of production is socialist mode of production, where markets, private ownership, commodity production, wealth accumulation get all done away with for planned for-use production.
I think I'm pretty well read on capitalism, socialism, communism, and even anarchism, but then a simple comment thread makes me realise I'd need to read 10x more just to follow along.
Nah most theory is theory and not practice. Read the big ones and worry about the details after the Revolution, they'll have to adopt to needs first anyways.
Pretending otherwise is where you get into trouble.