Is this an intellectual leap aiming to make the field more cohesive, like the quest for unifying theories in physics?

That is one of the goals, yes. In addition, it seems like you get neural architecture search (architecture is optimized), faster training, inference and interpretability. I'm working it out as we speak.

Ironically, convolution provides some unification in physics too, e.g. renormalization is a convolution.

Interesting, please do elaborate...

I read it as a riff on “monads are just monoids in the category of endofunctors”, but maybe that wasn't intended.

It kind of is. The commenter has been working on this formalism for a year or more. I'm sure he will come by with his link for the Discord channel where he discusses with and finds collaborators soon.

I has been less than 9 months. But yeah there is a discord if you want to follow progress https://discord.cofunctional.ai.