Socialism means the workers control the means of production which is an antiquated term but can definitely mean direct ownership of businesses. So worker coops are certainly socialist. It doesn’t really make sense to speak of socialism as a single system since it’s more of a collection of ideas, most of which having never been tried. I assume you are talking about the USSR and those who followed its economic system. While I agree that that system was bad, they also didn’t grant workers real control over the economy and weren’t really socialist by the original definition. Even Lenin referred to their system as state capitalism, which they advocated for because marxists believe that capitalism has to advance to a certain stage before socialism can take root. The stated plan was to eventually move towards socialism but of course they never did because when do dictators ever want to give up power?

Most people think socialism is about free markets vs state planning but this is just Soviet and US propaganda. While some socialists did advocate for state planned economies, you can also have state planned capitalist economies such as the nazi war economy.

Anyway, that’s all esoteric political theory and not super relevant to worker coops which almost everyone agrees are pretty cool.