While Latin has indeed evolved very little after it stopped being a native language, its vocabulary had continuously expanded until 2 centuries ago.
Until around the beginning of the 19th century, Latin had remained the most important language for the publication of scientific works and for international correspondence between well-educated people, and during this time many words have been added for naming things unknown to the Romans.
Also the preference for various grammatical variants or for certain word orders has been strongly influenced by some features common to the evolution of European languages, so a Latin text written during the Middle Ages feels quite different from a text written during the Roman Empire.
The use of it by the Catholic Church means its vocabulary continues to expand. After all, it’s necessary to speak of the modern world in church documents whose official version will be in Latin.
> Latin had remained the most important language for the publication of scientific works and for international correspondence between well-educated people
That is right, but while I have found it very useful even today to read in original the works of Georg Bauer, Newton, von Linné, Gauss and the like, there is much less interest in reading the many ecclesiastic documents that treated subjects with only a limited temporal relevance (unless you are a historian of that time period).
In general, I strongly recommend to read carefully in original the scientific literature of the 17th, 18th and 19th centuries, even if that requires the ability to read at least Latin, German, French and English, because by reading the original sources you can find frequently that the authors have said things quite different (and wiser) than what it is claimed that they have said in many university textbooks or popular science books.
In science and technology, there is very little that becomes truly obsolete, because the optimal solutions for solving practical problems often cycle through the space of solutions during the years, depending on how the balance between various advantages and disadvantages changes with the evolution of the available technologies. So those who believe that it is enough to read the up-to-date literature are typically wrong, because the miracle new solution of tomorrow is frequently again the same that was best 50 years ago, or even earlier, but which had become forgotten in recent years.
> there is much less interest in reading the many ecclesiastic documents [...] In science and technology, there is very little that becomes truly obsolete
Documents that contain administrative minutiae or legal rulings or whatever may only have value for historical study, yes, but one major reason for the very existence and authority of the Catholic Church is to serve as guardian of her doctrines and their development, and to communicate them faithfully across generations. Meaning, the doctrines of the faith are never made obsolete, or else the faith, and certainly the authority of the Church, is undermined. The understanding of them can be deepened and expanded over time, but the doctrines themselves are fixed.
I think of it as reading the very best writing, e.g., Charles Darwin, and not just another paper or book. Wouldn't you love to have a conversation with Darwin? That's what you get when you engage with their writing.
Until around the beginning of the 19th century, Latin had remained the most important language for the publication of scientific works and for international correspondence between well-educated people, and during this time many words have been added for naming things unknown to the Romans.
Also the preference for various grammatical variants or for certain word orders has been strongly influenced by some features common to the evolution of European languages, so a Latin text written during the Middle Ages feels quite different from a text written during the Roman Empire.