Is it permissible to engage in dhikr (remembrance of God) and listen to the Qur’an at the same time, considering Allah’s saying: "And when the Qur’an is recited, then listen to it and pay attention that you may receive mercy"?

Scholars differ on the ruling concerning listening attentively to Qur'an recitation outside of prayer. The Hanafis are of the opinion that it is obligatory, citing the verse: ﴿وَإِذَا قُرِئَ الْقُرْآنُ فَاسْتَمِعُوا لَهُ وَأَنصِتُوا لَعَلَّكُمْ تُرْحَمُونَ﴾ (And when the Qur'an is recited, then listen to it and pay attention that you may receive mercy). Whereas the majority of scholars hold it to be commendable, interpreting the verse as applicable only during prayer. It is more appropriate for one who intends to listen to the Qur'an not to engage in anything else, out of reverence for the word of Allah. However, if one does not intend to listen, then there is no harm in occupying oneself with dhikr (remembrance of Allah) or similar acts. Sheikh Saad Al-Khathlan pointed out that attentive listening is only obligatory in prayer, and outside of prayer it is commendable. If one intends to listen attentively, one should not engage in anything else. But if one does not intend to do so, there is no harm in occupying oneself with dhikr or other things. As for long pauses between verses, there is no issue in occupying oneself with dhikr or istighfar (seeking forgiveness).