Thanks to /u/gynnis-scholasticus for the summons. Speak of the devil (or folklore) and he shall appear!
Let me know if you have additional questions. I call to question your dismissing a belief in a historical period by saying it may have been "just a weird belief like aliens are today." Beliefs in historical periods are exactly like the belief in aliens today. That is an aspect of modern folk belief. Like all beliefs, there are adherents and there are skeptics, but folklore persists. Everyone has it, even when they do not recognize it as such.
Part of the answer that our friend has linked to consists of the following: Regarding whether people believed in dragons, the same could be asked about giants. I can address this from the point of view of the pre-modern European folk and how they thought about dragons (and giants for that matter). We can use that perspective to project backwards to gain some insight into the medieval point of view. That method is not without its flaws since traditions by nature change, but the pre-modern perspective can be useful in shaping an understanding about what the nature of its medieval counterpart.
First of all, it is important to understand that from the pre-modern European folk point of view, dragons (and giants for that matter) were not something that anyone normally described as actually seeing. People told legends (narratives told generally to be believed) about encounters with ghosts, fairies, mermaids, etc. because these entities were thought to co-exist with people contemporaneously. Dragons and giants were generally relegated to distant places or the remote past. They told stories about them, but only in how they were part of the historical record or about how people far away encountered them.
Part of the reason for this was practical: one can fathom a world being shared with extraordinary entities that could hide in "our present world." These included creatures of human or smaller size or creatures capable of invisibility. It was not easy to imagine large creatures existing in the world and not being seen by everyone. A dragon (or a giant) in the neighborhood is hard to overlook. The folk used a type of logic: fairies and ghosts can hide in our midst, but dragons are large and destructive enough so that they would be immediately discovered; we have not discovered any dragons in our midst; therefore no dragons must live around here, and they seem to exist only in the past or far away.
The folk described dragons in their historical legends and in their folktales (narratives that draw on folk belief but are told as fiction). In these stories, dragons are large and menacing, but a hero can kill them. Granted, that hero may have extraordinary abilities, so the dragon can be graduated in size to represent a heroic menace. The answer, I believe is that the folk tended to imagine a dragon as very large - elephant sized perhaps. Medieval artists often depicted dragons as much smaller - as you indicate. I suspect (but do not know!!!) that the medieval artist was asking the same question: how realistic is it for a hero to kill a beast that is overwhelmingly large. Pragmatism and a goal to be realistic may have down-sized the dragons. I have seen those painting, and they have struct me as wrong after having read folktales about encounters with dragons.
Some time ago I answered a similar question by linking to an old u/itsallfolklore answer, with u/epicyclorama making important corrections