Is the recitation of verses from the Holy Quran before the Friday sermon an innovation (bid‘ah)? And is it permissible not to listen to it by engaging in the recitation of other verses?

It is not appropriate to raise one's voice with the Quran on Friday before the sermon. If someone does raise their voice, then a person has the choice between listening or reading themselves, as both are permissible. It is proper to caution whoever raises their voice with the Quran before the sermon.