The labor theory of value has nothing to do with collecting profits and isn't concerned with who gets it. It argues that the economic value of a good or service is determined by the total amount of "socially necessary labor" required to produce it. (https://en.wikipedia.org/wiki/Labor_theory_of_value)

My point is that value is actually not determined by "socially necessary labor" but by supply and demand, even within a commune. The food you produce will rot if you and others produce too much of it = it has no value, and nobody collects profit (not even in the form of social capital) because everybody lost any possibility of selling for a good price by producing too much.

On the other hand during a shortage people will start valuing food much more than they previously did, gradually paying higher price as they have less of it - again totally disconnected from the "socially necessary labor" required to produce it.

Most importantly - the value of most if not all things is subjective and different based on time, place, etc. Even within a commune - some people simply don't like peppers, so even though you put a lot of work into them they have no value to these people (which will quickly change once there's a food shortage).