Believe me, I’m not conflating Capitalism with markets. Capitalism is a specific form of market economy by which individual Capitalists buy and sell Means of Production, or Capital, by which they can pay Workers to use and create commodities via wage labor.
Examples of Socialist market economies include Market Socialism, a form of Socialism built on competing worker-owned co-operatives.
Examples of Socialist Market Economies do not include Capitalist Social Democracies, because the primary defining feature of Social Democracies is Capitalism with generous social safety nets, a kind of “human-centric” Capitalism.
You on the other hand are making the misconception that Socialism is simply when the government does stuff. You’re wrong, of course, as countless people here have pointed put.
Capitalism with regulation is still Capitalism. Socialism is when Workers share ownership of the Means of Production, simple as.