My opinion on this is a little complicated. The classic definition of Socialism is a system of production for social good, where the banks, factories, and industries are publicly owned and run for the betterment of society; as opposed to being privately owned and run for profit, and production organized to serve the profit motive under Capitalism. This implies on its surface that a centrally planned economy is socialist, while a market economy is capitalist, but things get messier than that in the real world. State Capitalist countries like South Korea, Singapore, and Saudi Arabia had centrally planned economies for decades, but they ran them for the purpose of building successful capitalist economies.

And no Socialist country has been purely planned- even the Soviet Union allowed farmers to sell food from their private plots at prices that the farmers chose. In the aftermath of World War 2, returning Soviet veterans often combined their savings to build cooperative factories that produced needed products, like consumer goods. The workers often elected a chairman of the factory, and paid him a much larger salary because they valued their leadership, or because he had the idea. These cooperatives were later nationalized by Khruschev, almost certainly to the detriment of the Soviet economy. When the cooperative sector of the Soviet economy was nationalized, economic planning became extremely complicated, and a lot of "grey market/second economy" behaviors popped up, like factories hitting their quotas early and continuing to produce goods to sell at their own prices on an unofficial market. In the end, the Soviet economy consistently struggled to meet the demand for consumer goods, which it might not have done if Khruschev hadn't nationalized the cooperatives. I could go on and talk about the success China has had since it pivoted to a mixed economy with a big market sector, starting with their success with the Household Responsibility System, but I don't want to ramble any more. My overall point is that centrally planned economies can accomplish a lot of impressive things, but having the state own every single little business can cause problems. I think a mixed economy can work well under Socialism. Personally, I like the idea of using what Richard Wolff calls Workers' Self-Directed Enterprises for sections of the economy that might not work well under planning. I also think a company like Huawei provides a potential model for how worker-owned companies in a market sector might be run under socialism.

Of course, everything I just said about the Soviet economy occurred in an era before supercomputers, so who knows if a similar economy would run into the same problems today.