What is the ruling on saying "Hasten to prayer" (Hayya 'ala al-Salah) and "Hasten to salvation" (Hayya 'ala al-Falah) in the Adhan, and does the ruling change if we explain the difference in meaning?

The Adhan is one of the great شعائر (rituals/rites) of Islam, and it is obligatory to preserve its words and protect them from distortion. Many scholars have concluded that an error in the words of the Adhan or its performance in a way that changes the meaning invalidates it. Jurists have explicitly stated that the Adhan is invalidated if its meaning is altered by لحن (intonation/melodic error), لثغة (lisp), or لكنة (accent), and they warned against errors that invalidate the Adhan, some of which, if done intentionally, can even lead to disbelief. Therefore, if the muezzin is unable to perform the Adhan free from errors that change the meaning, he must be replaced with someone who can.