Data Science Take Home Challenge Interpretation of Question
Second one but dont stop there.

First of all you specifying if target_metric > x: engaged is just wrong and you have to let data tell you this x, not you choosing it.
Second one seems nice I would start with that, do some extensive analysis and only then start finding x empirically. How? just of the bat you can pose it as minimization problem for different x and find the one that has biggest purity/separation between classes.

Why dont stop there? There is no wright and wrong, if you have some plausible approach in theory but it fails in practice I would definitely
include it and elaborate on it, discuss it etc...