"This idea of the human essence is found throughout Marx's writing."
but I am not sure how much light this sheds.
If the essence is the relations but the relations are different in different epochs/ at different levels of technique/ then the essence changes. Since the usual understanding of essence is that it is unchanging, does the concept of 'relational essence' (an oxymoron?) help.
Is there an unchanging human essence in Marx? Only in the most abstract terms: men rework nature and in doing so enter into definite relations one to each other. But that is so vague as to be a truism. Once you go further and specify the social relations that men enter into, you are pulled in the direction of what is distinctive about men in different epochs.
Of course it is true that men never finally escape their human biology (only alter it), but that would be what was not their human essence but their animal essence. Defining the human essence it seems to me must escape us since it is necessarily without limitations, rather like trying to define freedom, which would only be to remove its scope.
Maoist Classicist scholar George Thomson's book The Human Essence is very good on this, but not convincing in the end.