I say, and with God's success: Playing the Quran from a phone or other device is merely a recording of it, not the real thing, so its rulings differ from those of actual recitation. It is permissible to play it while being otherwise occupied in general if one benefits from it in that way. We must strive very hard to listen and pay attention to it to gain the greatest benefit from it; because it is the word of God Almighty, and all of it contains advice and wisdom. The reward for the listener and the one who pays attention to it is very great. It is permissible in your case to play the Quran alongside other things as long as you are benefiting from it, and God knows best.