It's useful to note the title of the paper: What’s your (sur)name? Intergenerational mobility over six centuries. This paper is not tracking wealth, it's tracking income via tax records. It notes things like people who are lawyers or bankers now were more likely to share surnames with people in similar professions in the 15th century. It is not tracking inter-generation transfers of wealth.
In fact, qz even drops the most interesting conclusion in the article, which is their measurement of changing intergenerational income mobility overtime. They measure inelasticity at > .8 in Renaissance Florence and a generally static society until the industrial revolution, with inelasticity coming down starting in the 20th century.
The article isn't about secret trusts set up by the Medici, but the more prosaic fact that if you father and grandfather were lawyers, you're more likely to be one too. Still interesting, but it's not evidence that families were "able to maintain their wealth" through revolutions at all.