I enjoyed an anime called 'Im a spider, so what?' where the main character gets transferred to another dimension, except as a spider.
She's a genki girl in the anime (hyperactive trope) but only when she is alone. When she talks to others, she's an introvert (very terse and soft spoken), which is an interesting version of the trope. The only name she goes by is Kumoko (rough translation: Miss Spider, or maybe Spider-cutie).
In the original source material (the original Novels), she's fully an introvert. But I think the problem with anime is that acting in front of an audience is innately an extrovert activity.
Introverts can be side characters in an anime (Rei from Evangeleon, Nagato from Haruhi), but since they sit around and think to themselves so much it's hard for them to be a main character. Kumoko is an interesting way of doing it, since she is only hyperactive when she is alone.
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Mild spoilers: but the people who got transferred over got forms that best represented their soul. Most became a human again, but a few swapped genders and another few became monsters.
In the case of Kumoko, her introverted nature matched the spider the most. In contrast, teacher has the 'young at heart' trope and thus the teacher got the form of an elf, for example.
As an Isekai novel / anime, it's fantasy + sci-fi. They are all clearly in some kind of techo-video game world, but magic seems to have been the cause for how they all got trapped in the first place.