If you could sit with the authors of this paper and let them know this valuable insight, what do you think they would change about their paper and its conclusion?

Yes, but this is literally a study trying to determine whether correlation is causation.

I'm not sure they are able to disentangle it from general lifestyle changes someone on a new weightloss drug might want to make?

(However, you can probably compare it to other lifestyle changes people on previous weightloss drugs did. If we presume that going on a weightloss drug at all is roughly the same impact on associated lifestyle change choices.)