The question "how would communism look like / function" (which is what your question boils down to) is the most difficult one because the correct Marxist answer is "we don’t know". We cannot predict the future.

However, we can theorize based on current conditions. To answer "why would people work for free" we can look at volunteer work, of which there are so many! People volunteer to write wiki pages, make mods for games, but also to work at soup kitchens or community gardens. There are several aspects to why people volunteer. It might be fulfilling creatively, or they might be community expectation around this work. If you lived with others im sure you had to do a round of chores.

So this is how I see work in a communist society. People do it because it is either fulfilling or there are certain community expectations around it.