Promoting research papers with targeted ads
Actually the practice is old, though using Facebook may be new. My old alma mater regularly sends out publications and news items "promoting" research at the university. I think the intent is more to promote the university itself, however, though some of the news items are worth a look if the research suggests new breakthroughs in, say, medicine. And, I suspect that the practice has always included a certain amount of "targeting", though using older technologies. A special newsletter for billionaire donors, for example. 

But, yes, there are ethical issues, and the university needs to consider the impacts of such things. I have doubts about "using a project's money". I don't know if that was the case or whether it was just the normal PR practice from funds allocated for that. And promoting dodgy research would have serious ethical implications, of course. 

Note that my alma mater is a large US State funded place (an R1). In a sense, what they are doing is saying to the general public: Look at us, we do great things here. 

And that same general public actually provides serious funding for the place via taxes and grants. So, pretty natural, so far as that goes. In fact, not reporting back to the public in some way about how the money gets spent would have its own ethical issues.