Leaving aside that market socialism also exists, in which shares do as well, not just Marxist Leninist, what do you define as ownership then? Especially in today's age where value is in software not only hardware. How would a worker own a means of production?

In today's age of exclusive capitalism? There is no worker ownership of the means of production. If you can't use a mine to get some coal, or use some tools to make widget, or use a GPU to do inference I guess, then you don't own it, do you? The point is anyone who needs to do those things can, and that ownership is tangibly available to everyone. Not in the "this is public property" but the state actually owns it sense.