I know a brother who plays a game where while he is collecting items he randomly sometimes gets a charm and he can’t throw it away so instead he just leaves it in his bag and never uses it or anything like that. Is this allowed?

I know that you suffer from waswas; therefore, we always advise you to not pay so much attention to these things or focus on them. When you do so, we will simply tell you to avoid it altogether and find something else to play with. But when there is something that is fleeting and you just ignore it—and as you said, he doesn't see it or use it—then insha'Allah, when he avoids that which is forbidden, he can continue.