Well, I'm a medievalist and my specialty is the fifteenth century, so...hopefully, quite a lot? Hahaha.

More seriously, though--there are a few things going on here: the myth of medieval stasis, the difficulties of historical periodization in general, and the specific problems of "the Renaissance."

One of the problems in thinking about a historical era with any kind of modern pop culture presence is the difference between "accuracy" and "authenticity." That is to say, what feels right to us is based on the accumulation of modern interpretations of medieval/medieval-seeming things--LOTR, Game of Thrones, Kingdom Come, Sword in the Stone, "once upon a time," children's Halloween costumes, and so forth. This impression will have some similarities to the past, but it won't be identical--it will reflect our modern concerns, what we want/need out of the past, instead of how it actually was. Hence "authentic" in feeling, but not necessarily "accurate" in fact.

For a span of time like the Middle Ages--a thousand years! An interconnected world occupying part of three continents!--one of the major distorting results of the preference for authenticity is "medieval stasis." That is, we have an idea of ONE Middle Ages, one type of Middle Ages, with knights and castles and princesses and a belief in dragons. But in addition to not actually reflecting any one moment in the real Middle Ages, this monolithic "authentic" view is frozen in (fictional, or "pseudo" if you want to be Richard Slotkina about it) time. It doesn't capture the fact that the world changed radically between 500 and 1500--all the while still being "middle age" in the sense of occurring between the Roman Empire and what a handful of Italian elite men flattered themselves as being an intellectual revival of Roman ideals. And the world entered that time period changing, and continued to change afterwards.

And not just change in a vacuum, but grow on its earlier self. That's why it's hard to draw a firm line between medieval and early modern (we'll get to "Renaissance"/rebirth in a moment). A lot of the things that we'd call "early modern" are medieval or late medieval in origin. Like, we'd say urbanization and the prominence of cities are very early modern--but this is a process that began in the eleventh or twelfth century in Europe; earlier (or never stopped) in the Near East. The Low Countries (Netherlands &c) are superstars of the early modern global economy--a position that began in the high Middle Ages. European imperialism expanded European political and religious domination far beyond a western European hub--a process occurring from the 15th century, the 12th, the 10th, the 6th depending on your point of view.

Now, all those things are probably not what you mean when you say "medieval"! That's the authenticity versus accuracy problem, because they are all very definitely happening in the Middle Ages. So let's consider--Neuschwanstein, the prototypical medieval "fairy castle," was built in the 19th century. Even Versailles is 17th. Soldiers were fighting with swords on horseback in World War I! Even after the invention of the printing press, handwritten notes and documents continued in dominance in a lot of cases probably until the rise of the affordable PC and (especially) cell phones. Universal literacy even in western Europe wasn't achieved until the 19th century.

Obviously, a lot also changed in that time. The point is--it's impossible to draw a single clear distinction between "medieval" and "early modern" and then point to elements of each that sneak into the other. That's both the problem and benefit of authenticity. It allows us an easy shorthand for understanding that the world did indeed change over time, but it's too easy.

The "Renaissance" muddles the picture even further. Once upon a time, "Renaissance and Reformation" was shorthand for the period of time after the Middle Ages. "Early modern" is a much more recent invention as a term. Part of the reason it has gained prominence is that scholars recognize just how limited the "Renaissance" was in its reach. We're really talking about a handful of elite Italians first, some Germans, and eventually French, English, some Spanish &c, mostly men but a few women, and wildly upper-class, urban people involved in an academic, artistic, and architectural movement focused on a particular type of revival of Roman tradition. (Of course, the twelfth century and the ninth century had experience their own versions of a Greco-Roman rebirth!) Eventually, yes, the same impulses that drove the Renaissance would swell up among other segments of the population, which is a big part of why today it seems like the Renaissance is so much the roots of the modern world. But as far as the early tinges of it go, it seems surprisingly isolated.

In fact, you could even go so far as to point out that if the Renaissance artistic and intellectual movement grew out of the late fourteenth, fifteenth, and sixteenth centuries, it itself is medieval.

I know this isn't a neat list of middle-school-style textbook "vocabulary word" entries delineating what is medieval that still existed in 1600. Unfortunately, it's only pop culture that plays by those rules. History is a mishmash of "change and continuity," and periodization is one of the messiest (but necessary?) results of trying to deal with that.