The setting of the story was probably in a futuristic modern city, and the omnari is going in the forest to scavenge for her ancient history. The mood of Omnari seemed to be bored and impatient. She had sped up, as if she was trying to finish her task as soon as possible. She didn't want to participate in the scavenger hunt but she had no choice. Her teacher had assigned her to do the activity. So, Omnari had started her task immediately so she can finish sooner.
And the reason you can tell the character is bored is because in the text is states "sped toward the island, increasing the speed of her Hover-Ski "
and "blinked to take an EyePhoto, checked her list, and headed toward the crumbled city in the distance."These two phrases show impatience of the character. It also says in the text "boring scavenger hunt her ancient history teacher assigned."