Generally this is the answer when there's an announcement like this. Some early paper or analysis showed some (often weak but potentially very interesting) correlation between $new_drug and $scary_disease/$scary_disorder. Doctors and scientists go off and study that in more depth with better controls or more data points and we learn a little more about the world, if you miss the initial paper(s) the follow up can seem a little random.

I don't think there's a confirmed mechanism (or even whether the fact that it does prevent dementia is a confirmed fact).

But you could speculate that obesity -> cardiovascular issues -> neurological damage, and that could explain things.

We don't know the "how" in a surprising number of medicines.

We unfortunate know very little about how dementia / Alzheimer's develop in the first place.

This new study that did not find a causal link was part of the attempt to find out how. The original study was more of an observation than a deep dive.

You could think of it similar to a study that shows something like "People who don't watch network TV have fewer strokes", which could be an interesting correlation, but the causal effect might be something more like "people who are more health conscious tend to avoid sitting down for extended waking periods" which ultimately has nothing to do with TV.