Caution: Translations of Quran and Ḥadīth may lead to possible misapplications and misinterpretations. This site is intended for students of sacred knowledge that are proficient in comprehending classical Arabic and have a strong foundation in Islamic sciences. Also note that religious injunctions rely on several aspects beyond what one may glean through reading individual aḥādīth.
quran:7:204

So when the Qur'an is recited, then listen to it and pay attention that you may receive mercy.  

And when the Qur’ān is recited, listen to it and pay heed, ˹refraining˺ from speech, so that you might find mercy: this was revealed regarding ˹the requirement of˺ refraining from speech during the ˹mosque˺ sermon, which here has been expressed by ˹the recital of˺ ‘the Qur’ān’, because it ˹the sermon˺ comprises it; others say that it was revealed regarding the ˹requirement of silence and attention during the˺ recitation of the Qur’ān in general.
القرآن:٧:٢٠٤

وَإِذَا قُرِئَ الْقُرْآنُ فَاسْتَمِعُوا لَهُ وَأَنْصِتُوا لَعَلَّكُمْ تُرْحَمُونَ  

{وإذا قُرئ القرآن فاستمعوا له وأنصتوا} عن الكلام {لعلكم ترحمون} نزلت في ترك الكلام في الخطبة وعبَّر عنها بالقرآن لاشتمالها عليه، وقيل في قراءة القرآن مطلقا.