What is the ruling on the action of one who deliberately made a sound to break the silence, and does not remember whether his action was before or during the imam's recitation of the Holy Quran in the Isha prayer broadcast on television, and is he considered sinful for doing so?

If you did not intend to distract people from the Qur’an, then there is nothing against you. Listening attentively to the recitation of the Qur’an is desirable, not obligatory, according to the majority of scholars. It is not obligatory to stop speaking during the Adhan (definition) and Iqama, or when an Imam recites if you are not following him in prayer. It is obligatory to listen to the Qur’an during prayer with the Imam or during a khutbah (definition) (sermon) that you attend.