Someone in the 1700s was like "Mm... I think I'll make an old-style rapier based on 1400s German Rapiers." and then did that thing.
And that piece is now in a museum 300 years later.
This is not rocket surgery.
For the person in the 1700s to make a rapier in the style of the 1400s there had to be a rapier in the 1400s with a style to mimic.
And -specifically- a German one.
No, it just requires the "private donor" to donate a weapon in the museum called Rapier in the 15th century century German Style, probably made in the 18th or 19th century. Which, by the way, is a period of time in which historical knowledge of weaponry was weak and beset with all sorts of myths. for instance, that same person might have claimed something like medieval swords were essentially blunt metal clubs, which is untrue but was widely repeated in the 19th century.
But in actuality, I'm pretty sure it's just a rapier with some characteristics that were identified in specimens of German swords, and it was called a rapier, because this sword is a rapier, or it was modeled after a cut-and-thrust sword from the 15th century that someone called a rapier, and they called it a rapier in an imprecise way, because in the 19th century there weren't sword typology cops to stop you.
To be clear, this sword was made 200 to 300 years after its supposed inspiration, and doesn't actually look like any 15th century sword I've ever seen. I challenge you to find a "German rapier in the style of the 15th century" that is from the 15th century. German fencing in that century focused on the longsword. A 19th century swordmaker making a weapon styled after a "15th century German rapier" probably just made an edged rapier with a ring-guard. This precise example has a curved hilt going each way, like an older sword, rather than a characteristic basket or wire hilt, like a contemporary rapier. It is inspired by 15th century weapons, purportedly German ones, but isn't modeled after an actual rapier, which did not exist in that time and place.
This is quite a thread drift, but I really want to emphasize that 15th century German fencing did not involve rapiers, it focused on pretty much exactly the AD&D weapon list. Longswords, dirks, early broadswords, early two-handed swords, and a handful of transitional cut-and-thrust swords in the Romantic style.
This is a German sword from 1440: