No marketing team would willingly do this and it's insane to think otherwise.
Insane is a bit hyperbolic. The history of marketing is full of grand mistakes that seem absurd in hindsight.
Of course, they would. If the administration asked Bezos, and he gets a benefit out of it. He will task his marketing team to come up with something which tries to frame it in a positive light. Knowing that even if a few people make a stink this will blow over eventually and when it rolls out, he can always say it is just about puppies and neighborhood security. Nobody cares.
And yet this went up. I understand it’s easy to just say “marketing teams don’t understand anything,“ but I have worked with many and they are incredibly sensitive to negative feelings/reactions. They get it wrong but they tend to air on the side of caution which means the vast majority of the time they avoid situations like this incredibly intentionally.
Cambridge Analytica was an experiment run by a marketing team. I wouldn't say marketing will always side on ethics.
Propaganda is, and always has been, a subset of marketing aimed at shifting public perception. It would be wild to assume it never happens.