Outside of the Arthurian and other legends? Not that I am aware of. Swords in medieval Europe were essentially... not really disposable, but it was well understood that they would be damaged, require care and maintenance, and eventually break or wear out. Especially if they were used a lot.

Now, the interesting part is that with care and storage swords CAN last a long time. Especially if you are able and willing to replace different pieces of them, but not necessarily the whole sword at once.

So what this led to is that at some points during the medieval period swords were very expensive, and at other later points, there were so many of them hanging around that you couldn't give them away depending on where you were in Europe at the time.

The Arthurian legends are, as far as I know, the main source for all of the popular media in the west about seeking after a particular sword. However, they are NOT the ONLY source.

There are other legends as well. Beowulf's sword Hrunting. Other legends of powerful objects as well. Manannan Mac Lir gave Fragarach to Lugh.

Swords have long been a symbol of authority as well as a weapon. Part of this is because of the type of weapon they are, and part of it is because of who had them at various times.

Now, as to what warriors tended to value in swords, now that was rather different. Warriors needed a weapon. And so they valued good craftsmanship and good materials.

And what people thought the "best" of those things were, tended to vary based on where you were and when. But it is interesting to note that the places in Europe famed for their metalwork in the Medieval period also became major centers of trade.

So in Spain you have Toledo steel, in the Germanic states you have Solingen Swords, in Italy it was Milan that held supreme. In Britain, it was either imports or for local make you wanted London's Worshipful Company of Cutlers.

All of this is before we get in to the discussion of various developments of metallurgy at various times. For that, suffice to say that one of the main things that made the Medieval centers for sword and knife making as well known as they were was a very good control of the carbon content of their iron as they worked it in to steel. As well as knowing, at least somewhat, about certain trace metals that can make steel more suitable for most common applications at the time.

A lot of legends about swords that can cut through anything or otherwise are just better likely have their origins in the fact that metallurgy was not developed everywhere equally all at once. It developed over time with individual discoveries turning in to cultural traditions long before scientific methods or understanding could be applied. So if a soldier was traveling in a distant land and ran across metallurgy far superior to that in their own land, it would seem to have magical properties to their eyes.

Remember that the scientific method of exploration, at least the way we frame it now, dates to the 16th century and a lot of differences in knowledge prior to that were attributed to everything from divine favor to magic to whatever the flavor of the month was.