The concept of a task management app for children is dystopian. It's treating them like office workers from the beginning, and considering the example given is the typical chess, piano, Chinese lessons, it's just overloading the child for exhaustion.
Parents should be parenting their children. Limiting their exposure to things, including screens and the internet, and disciplining a child to study or work are part of a parents purview. I can't see why people even have children if they delegate all of their parenting responsibilities to screens and software.
Welcome to ADHD management. At its core, its an executive function deficit. My wife and I both have it (my case is worse) and so do most of our children. External systems and environments have a huge effect on our ability to manage life, and that's not something that can change. The solution is to learn to work with it and tune our environments.