That's a bastardized interpretation of what socialism is.
Socialism is defined by social ownership. The society as a whole owns production, rather than individuals or groups.
A coop is a just group that divides up ownership among all the workers, not the society/community. The division isn't necessarily even. And the workers don't necessarily have 100% ownership between them. For example, there are coops with publicly traded stock.
A coop can be, and often is, still privately owned.
If you're definition of socialism is "Workers owning means of production" (which by the way, is not and never has been the definition), then every FAANG is a socialist entity for awarding their employees shares.
There is a full spectrum of left ideologies that call themselves Socialist, so your claim of "is not and never has been the definition" is flatly wrong. Collectivists and Syndicalists, in particular, are Socialist schools that are strongly onboard with worker co-ops (typically described as trade unions running their businesses).
And FAANGS are not owned by their workers, full stop. Less than 5% of Google's shares are owned by employees, and most of those shares are owned by management. Bezos personally owns more Amazon shares than everyone else in the workforce combined, Meta is well known for being in a strange situation where Zuckerberg personally owns more than half of all voting shares. Vanguard owns more shares in Netflix than the entire workforce combined. Apple has negligible employee owned shares.
Your misinterpretation comes from a willful twisting of the words "workers" (does not typically mean "the founder personally") and "owning" (which is typically understood as "having control over" rather than "maybe could break the tie between a handful of investment firms").
Maybe more precise to say "not mutually exclusive with free market exchange", 'capitalism' (as a socialist would define it) is primarily an ownership arrangement.
