Answered by Shaykh Faraz Rabbani
Reciting the Qur’an While Busy

Assalamu alaikum,
Imam al-Tahtawi mentions in his Hashiyat Maraqi al-Falah,
“As for the reciting Qur’an while walking or working, if one is paying attention and is not busied by one’s work or walking, it is permitted. Otherwise, it is not.” That is, it becomes disliked, because we have been commanded to be attentive when the Qur’an is recited.
Wassalamu alaikum,