The paper is trying to explain some unexpected observations by the JWST. It starts with the idea that maybe these observations are dark stars, works backwards to show that there are a couple of models of dark matter where this would work, and then predicts that, if these really are dark stars, they'll have a measurably different spectrum than regular stars. Measuring the spectrum would then substantiate (or not) a model of dark matter. This sort of thing is how they might nail down a more likely model of dark matter.

This is not unlike trying to explain those observations with ordinary matter, working backwards to try and work out what distribution of ordinary matter could produce the observations and what sort of physics would create such a distribution.