Socialism means workers collectively own the means of production, and it isn't synonymous with central planning.

This can only be true if you stop thinking at the end of the sentence, without reading into any of the implications, or any circumstantial cause and effect.

If the workers collectively own everything, then that means that every worker has just as much right as anyone else to make decisions on how the process plays out. This means that the group has to come up with a way to make decisions. Since the group has to make a decision, and everybody has a right to make decisions, the group is effectively making decisions on behalf of those in the group.

If the workers collectively own everything, then that means they have to work together and organize to get things done. This means that the group has to come up with a way to organize. This means that the group will be deciding on behalf of those in the group what work is done by who.

If the workers collectively own everything, that means the workers have to decide what rules or laws to follow, and how to enforce them. So now the group has to decide by what convention it'll hold its members accountable. If it wants to hold members accountable, it implicitly has the power to do so.

A group with decision making power that enforces law among its members is a central authority.

A central authority with power over the market and all decision making is central planning.

Your description of capitalism legitimately sounds like mental gymnastics. You can call anything centralized if you reduce the context to only itself. That is dishonest, the context here is the market. If a market is centrally planned, then all aspects of the market need to be centrally planned by the same unit. That's what central planning means. A disunited group of private entities all planning things for themselves is absolutely not an example of central planning.