Akiyama was also a socially awkward person, so when Sharik invited her to the party, she became more talkative and got to know other people, even if it was just the people in Allen's circle. But that was more than enough for her, because Allen's circle consisted of various races, one of which was dwarves.
When she met Geirhild, Geirhild immediately invited her to be friends; because she was an other-worlder, they exchanged information about technology in other worlds.
In exchange for the information, Akiyama asked Geirhild to make her some equipment, one of which was the thread. She needed it for arrow adjustment and in case she used the arrow as a melee weapon.
