I struggled to find the meat in this article and a quick google of the terms involved only really brings back the same article, which is almost 3 years old now.
On top of that the story is a cookie cutter rewrite of every upcoming ML/math technique which are always poised to provide some amazing insight into the human mind.
A more honest title would be "algebraic topologists think algebraic topology is great, academics who have employed algebraic topologists want it to be great but don't really understand it".
Edit: for anyone looking for the actual meat this appears to be it:
Objective Morphological Classification of Neocortical Pyramidal Cells (2019)