That’s not really Socialism, though. Segments of an economy cannot be Socialist or Capitalist by themselves, just like an arm cannot be a human. They all exist in their contexts. A worker cooperative in an economy dominated by private Capital is not an instance of Socialism, as it depends on the broader Capitalist system.

Socialism, in reality, refers to a broader economy where public ownership is primary, while Capitalism refers to a broader economy where private ownership is primary. All Socialist societies have had public and private Capital, and all Capitalist societies have had public and private Capital, it matters most which one has the power.

I recommend reading my post here on common problems people run into when determining Modes of Production.