there are regular swords, but the kingdom of rhyboflavin is a peaceful land that doesn't need warriors who would use them.
there's some dialogue hinting of a time of war and dragon slaying, Prohyas and Vambre's mother was a famous warrior who used Magiswords before settling down at a broccoli farm and Prohyas telling Vambre that nobody in their lifetime fought dragons. in the case of Grup (the warrior's blue dragon pet) and Prug (Grup's brother) when they were first found they were living in caves and were also harmless and very low level threats.
in the adventure academy shorts there's more infodumps about dragons, warriors and the past, how there hasn't been a dragon sighting in years, families that are famous for their histories of adventuring and all the outdated survival lessons.
another neat thing in the background is a screenshot of the map of Lyvsheria where the four courners surrounding the land are labeled as "weird stuff" and "really bad news". oh, there's also a giant sleeping face in a desert called the barren faceland, if it wakes up it's said that something terrible would happen, or the end of the days.
that's all the info I have about regular swords in magiswords.