TL;DR The fediverse represents a socialist philosophy in that these servers are not all administered by a centralized authority, but by the individuals who put forth the labor to bring them into existence.

Socialism doesn’t necessarily have a strict definition. There are some who assert such definitions, but take the work of Karl Marx, he wrote a criticism of capitalism in an analytical fashion. There’s Marx-influenced socialism, but to say “Marxism” is a little misleading, because it’s not like he proposed an exact plan for how to run an economy and government, rather he discussed the problems with how we assign value to labor.

In general, and in my opinion, socialism as a broader philosophy is the idea that society should be constructed in such a way that it behaves in the interest of the people. In other-words, the goal is to design functional social systems that can ensure equal rights to a high quality of life, while also incentivizing and rewarding participation(I know many suggest that modern capitalism does this, but it doesn’t).

So, in the case of social media and the fediverse, these federated networks are comparable to social systems that are operated by the public, governed by the public, and funded by the public. Therefore, see TL;DR.