You can have full blown worker coops in the capitalist system, the question is if they are state mandated or not.
The definition of socialism isn't any sytem with a good outcome for workers.
I 'm not sure I understand the question? Socialism is a political philosophy on how the state should operate and what it should permit. It IS a description of the states behavior.
Democracy has nothing to do with it. You can have a socialist country with a king, or with direct democracy and no leader.
You can't have a socialist state without socialist laws and rules.
People refer to systems which apply socialist thinking as socialism, even if the governance is not a state government.
For example, let's say a theoretical union takes guidance from the political philosophy of socialism, and requires union members to contribute the highest percentage of their salary as union dues, that they can legally get away with. Let's say workers are paying 90% of their salaries in union dues.
The union can then use those dues to support the union members in various ways.
This isn't a state government, but it behaves like a socialist system and people would probably call it an example of socialism.
The wikipedia page on [religious socialism](https://en.wikipedia.org/wiki/Religious_socialism) even has some examples of this in religious communities.
You also have socialist anarchy, which supports stateless socialism
Realistically that seems to be more or less completely unsustainable without some use of force. e.g. if individuals who contribute more than they pay in are allowed to opt-out the system quickly collapses. That's how universal healthcare, state pension/social systems work etc. so it's not necessarily a bad thing. However in general socialist "corporations" are generally incapable of competing in a "free" market so they can only exist when they are supported by the state or private/capitalist enterprises are banned or strongly restricted in one way or another.
Sure, that's why I said this was theoretical. I wasn't using it as a demonstration of how socialism can be sustainable without a state, I was using it to demonstrate a system that might be described as socialist even though it's stateless.
You can have a democracy with 51% ruling and 49% in chattel slavery and poverty (but having a right to vote
I would agree that socialism isn't compatible with private property and civil rights as we commonly understand them today (in the US).