Big fan of japchae. However, I think this recipe has too many ingredients in the pan at one point: ground meat, onion, carrot. Then you add the mushrooms so the mushrooms basically steam and don't get any chance of browning. And the carrots already soften when you add mushrooms. If you wait until the mushrooms are cooked through, the carrots may turn into mush.
The general process in japchae is to take on each ingredient one by one: Stirf-fry onions first -> transfer to bowl -> stir-fry mushrooms -> transfer to bowl -> stir-fry carrots -> bowl -> stir-fry meat -> bowl. The order is not set in stone, but the key is to stir-fry each ingredient separately because each requires different cooking time.