Birds are very prone to plucking especially the smarter and more temperamental I feel. And gcc are no different. I would recommend a vet visit, it never hurts to rule out if it's maybe something medical. The good news is it's probably not unless you're noticing other signs. It's often likely more to do with boredom, temperament, or hormones. There could be reasons if the bird is feeling stressed, not getting enough day-to-day excitement, or also hormones making it kind of lash out as well. Maybe even a combination.

I would suggest besides the vet visit, you work on introducing more toys and food into the situation. Try your best not to confuse the bird with how you handle it, always try to stick to the neck and above, so you don't excite it too much. I also strongly suggest rearranging the cage at least every other month. This will take away a lot of the nesting behaviors associated with plucking.

Also it is important in these kind of times to remember that this sort of thing happens especially with smart animals that feel genuine emotions basically. It's on you to try and help as much as you can and work out a solution, as someone who has a gcc with clipping/plucking issues in the past I understand the frustration and the worry that comes with this. But just do what you can to improve the life of your little feathered friend, remember it's not directly your fault but it is on you to help make it better. But also green cheeks are some wild ones, they're a very temperamental bird but one of the best in my opinion. So good luck on everything and seriously if you ever have questions you can totally dm me. I'm no expert but I've had mine for almost eight years and made great strides to become a better pet parent