I don't care what the writers say, Sora's golden plates on her left arm is actually a prosthetic. Think of it like how Bucky has his silver arm in the MCU, but Sora has hers because of a terrible mech racing accident. Her entire arm from her shoulder down got extremely dislocated and mutilated when her mech crashed with another's, and it had to be amputated (on-the-spot --- sorry) in order to save her life. Being the genius resourceful tech-girl she is, Sora then builds her own robotic prosthetic arm. Arin is with her through it all, of course, and helps her build her arm and do other things that require both arms.
Since Sora's dominant hand, her left, got amputated with the rest of her arm, she had to learn how to write with her right. It's not as well as her left, but it does make her ambidextrous.