Is saying "I bear witness that Muhammad is the Messenger of Allah" and sending blessings upon the Prophet upon hearing the adhan considered a "bid'ah" (innovation)?

One must adhere to the prescribed legal supplications (adhkar) and prayers (du'as) that are specific to certain situations, as they were revealed in the Quran and Sunnah, without addition or subtraction. This is because the wordings of the adhkar are divinely ordained (tawqifiyyah) and possess their own characteristics and secrets. This is demonstrated by the Sunnah of the Prophet (peace be upon him) in his teaching of the supplication for sleep and in his response to the muezzin. The Companions and jurists have agreed on this matter. Reciting blessings upon the Prophet (peace be upon him) is among the best acts of drawing closer to Allah, but it has its legally prescribed places, and it is not permissible to add it in places where the Sunnah did not mention it, such as mentioning it while repeating the adhan with the muezzin.