With the Adoption, this was included so amazing work. The artist is Yatozaa; the link is here https://ytzcommission.carrd.co/

So her swords are very rare. Any high noble could get are called "Bonding Swords". They bond to the owner with the ritual cast upon them, and the swords belong to her until death. She can summon them when she needs them, and depending on the caster and their element, they can make your spells more powerful. The reason she couldn't use them when enslaved is that the swords had talismans that prevented her from drawing the blade, so it was an overly fancy club at best.
Ariana's sword was gifted to her on her 15th birthday, possibly by the Tundra family, since she was a top contender to join the family. Most mid-nobles or low nobles would use looted swords they obtained in her raids. All her people from the Nordic Kingdom are mostly warriors, but also blacksmiths and other craftsmen, to labourers.

The swords are like "Frost Brand" in Dnd. The difference is that she can use her swords as a spell focus and have her spells flow through the blades. Sadly, she never got the chance to learn her family's secret techniques and only knows the family's known styles.
Lastly, the more interesting fact is that Ariana was shocked to hear how Nobles get their spouse. For high Nobles that know combat, do a "Courtship" battle. While hers is similar, but the Male or Female would pick the ones they like, and those picked would have a battle royally. The last one Standing gets to marry into the family.