I think it comes down to whether you believe in market socialism or not, as market socialists and non-market socialists have a different understanding of private ownership. Non-market socialists, such as orthodox Marxists, see any kind of privatization as a negative and as such promote public ownership. Market socialists make the distinction between private ownership and cooperative ownership, because cooperative ownership still tackles the worker exploitation at a micro level. In a private ownership the worker is exploited because the owner of the means of production can use their power dynamic to exploit the worker but in a cooperative that worker is a part of the ownership which would mean exploiting the worker is akin to exploiting yourself. In that sense the worker-owned companies may not be compatible with orthodox Marxism, but they're still socialist in nature.

I will mention that it wouldn't be the final state of socialism, I don't believe we can switch to cooperatives and call it a day. Marx saw socialism as a process and we should see socialism as a process. Going from private ownership to cooperative ownership is just one small step in that process. There will be more steps in the future that might eventually end up looking more like orthodox Marxism. So I really don't see it as not socialist.