Agreed. She is in a totally different home with people she doesn’t really know. How scary this all must be for such a little girl. With time, however, she most likely will come out of her shell. As for eating and drinking, she may just be doing it when you are not looking. For the toys, that’s understandable; it will take her a little bit to get used to her new surroundings and then have any interest in playing in toys.
It’s only been a day, so I would definitely not even try to pick her up right now. She will most likely get freaked out, even if she does know how to perch on a finger.
The first step is to get her used to your presence. I’d give her several more days alone to herself, but after that, you can start to sit by her cage and talk to her. No sudden movements, and no reaching your hand in to the cage and grabbing her - this will all scare her. Just talk softly and quietly (obviously no yelling or anything). After several days of you sitting by her cage, she should at least get used to you being by her.
The #1 to remember when you have a new bird settling in - be patient. Do not force anything. This will just teach her to be afraid of humans.
I’m glad you want to comfort her and keep her happy, but at this point perhaps give her a bit of time to herself.
I wish you the best of luck with this little girl. Thank you for adopting her in to your home, and I hope you and her will become great friends over time.