Politics is when I make bad stuff happen to people I hate. So when bad stuff I helped cause happens to me, this cannot possibly be politics.

The word “Socialism” is too broad to be useful here, it can refer to democratic socialism, which is the dominant political stance in Nordic countries, so yes, market economies and social programs can co-exist.

Yugoslavia was a market economy in eastern europe under socialism.

There was a limited amount of pseudo-private “workers collective” (OOUR) companies starting from the mid 70s all the way to the breakup. It was certainly not a market economy in any meaningful way. The entire economy was propped up by foreign loans, which was a cause of so much inflation that the currency had to be re-adjusted twice, starting from the late 60s.