Style of referring to a cardinal

As I grew up, I was accustomed to referring to a cardinal by inserting his title between his first and last names. Thus, for example, I was confirmed by the then-archbishop of St. Louis, John Cardinal Carberry. This was distinct from the usage in the case of an archbishop (so, for example, the next archbishop of St. Louis, Archbishop John May). More recent usage that I've seen indicates that this usage seems to have been discontinued, or at least fallen out of favor.. The [official biography of the current archbishop of Newark](https://www.rcan.org/offices-and-ministries/archbishops-office/tobin-biography) refers to him as "Joseph Cardinal Tobin". But other carefully written sources such as the American Catholic magazine [*Crux*](https://cruxnow.com/cardinals/2018/09/02/cardinal-tobin-reportedly-declined-to-investigate-mccarrick-misconduct-rumors/) or the political journal [*The American Conservative*](https://www.theamericanconservative.com/dreher/cardinal-tobin-vigano-sadness/) use the phrasing "Cardinal Joseph Tobin". Is there a usage preferred or designated by the Vatican or a more local group of bishops? Or does it depend on a given style book?