Is it better to perform Tahiyat al-Masjid and listen to a fiqh lesson, or to continue performing supererogatory prayers (nafl) and reciting the Quran, knowing that the lesson includes mentioning the Prophet (peace be upon him)? And is it obligatory to interrupt one's Quran recitation when the Prophet (peace be upon him) is mentioned?

The best for the questioner is to sit in a study circle as a listener, because acquiring knowledge is better than supererogatory acts of worship, as stated by the scholars. As for interrupting reading or prayer to send blessings upon the Prophet, peace be upon him, when he is mentioned by the preacher, it is not obligatory, but if one does it, it is permissible.