It's just an algorithm. Not a big conspiracy. You can definitely influence in which folder you end up. Seems like Buttigieg's team has done a better job at it.
Sure, however this is the kind of cases where "the system" (democracy) would benefit from an equal treatment of all, regardless of their capacity to game gmail.
I did and I have gone through the mbox files and I cannot find anything that would explain the curious difference. That is not to say that there isn't a rational explanation, the probably is, but please give the study authors some credit. They aren't dumb.