It's funny because this is what first led me to this forum, and I just made a post about it right before seeing this

I've had my bird for about three months now, so one of the more experience owners might have some more useful advice.
I have a GCC, and when I first brought her home, she didn't really play with toys, and when she was out of her cage she was only interested in cuddling and wasn't really into exploring or playing games. She's still cuddly, but she is much more brave and spunky now. Trick training was extremely helpful. Just by following Michael's guides and doing a couple ten minute sessions a day, she would be distracted from cuddling for stretches of time, and learned do be a little more independent.
After teaching her to step up, I did target training with her on my shoulder. I taught her to target the stick a little farther down my arm each time, until I could reliably get her to step down. Then I started other tricks.
As for the toys, you might need to show her what they're for. At first, Luna was mostly interested in toys with ropes (because she likes to swing off of the drawstrings on my hoodies), but would only play with something if I was holding it. I showed her how to tear up paper toys, and got her interested in toys with textures by scraping a fingernail against them to show her how weird/rough they are. Getting her to play with them alone just took some time. I think it helped to have a good variety in her cage, and then if I saw that she really liked one, I would buy/make more that were similar but also different. Her favorites now are plastic bottlecaps. We wash and save them, and she likes to play tug-a-war with us and uses them as foot toys.
As for always wanting to be out of the cage and with you... someone else will need to weigh in on that one. My bird is the same way. There are times when she wants to be in her cage: she naps occasionally and sometimes wants alone time after a bath, but for the most part she wants to go wherever I am. Since I don't work at home, she's alone for part of the day, and I have a small apartment anyway, so I handle her as much as possible.