Making a profit is not capitalism.
I don't know how I can more simply state it. Capitalism=private ownership of a company/economy (that's te literal one liner google definition even more condensed). Think of it like democracy vs dictatorship. Democracy->workers control surplus (investors still get their investment back+interest--there are different models), dictatorship->an investor or a proxy investor controls the company, or an upper class within the company control the surplus and workers get a set wage and have no power.
Ultimately it's the relationship the workers have with what they produce.
In the google definition it gives state ownership as a 'rather than capitalism' example, but that assumes a non dictatorship where the workers collectives are actually autonomous and self governed. In the case of Soviets and China, however, the system of collectives was always centralized state-capitalism (and later full blown state sanctioned hyper-capitalism). But there are commie examples like in Spain, where are a huge system of worker run co-ops that have existed since the late 50s with roots going further back to anarchist run co-ops of the civil war. https://en.wikipedia.org/wiki/Mondragon_Corporationhttps://en.wikipedia.org/wiki/Caja_Laboral
I don't see why you are talking about the state.
I am trying to understand precisely why you would exclude worker-owned cooperatives such as John Lewis, building societies, lawyer partnerships, etc.
It appears your definition definition of capitalism is artificially narrow and instead of addressing role of capital, you are addressing ownership structure.
Ultimately it's the relationship the workers have with what they produce.
In the google definition it gives state ownership as a 'rather than capitalism' example, but that assumes a non dictatorship where the workers collectives are actually autonomous and self governed. In the case of Soviets and China, however, the system of collectives was always centralized state-capitalism (and later full blown state sanctioned hyper-capitalism). But there are commie examples like in Spain, where are a huge system of worker run co-ops that have existed since the late 50s with roots going further back to anarchist run co-ops of the civil war. https://en.wikipedia.org/wiki/Mondragon_Corporation https://en.wikipedia.org/wiki/Caja_Laboral