Yes it is common, just not always to the scale of a Veritasium video. Usually it’s just the press office for a university putting out a press release or a summary article in Scientific American.

But in the case where the story is interesting to a larger audience, having a push behind a story across non-academic media is not unheard of. If you can get some media coverage of an academic topic, it can be very beneficial to the researchers’ careers. One goal for a researcher is to bring notoriety to their research, to their institution, and to the field in general. This is the main motivation I see.

The authors may have pushed the arxiv paper out earlier due to the timing of the release of the video.