What is the ruling on saying: "Allahumma salli 'ala Sayyidina Muhammad (O Allah, send blessings upon our Master Muhammad)" in the Ibrahimic prayers, and does the prayer of one who says it out of ignorance of the ruling become invalid?

It is permissible to use the word "Sayyiduna" (our master) for the Prophet Muhammad, peace and blessings be upon him, for he is the master of the children of Adam. The Companions also used this word for one another, and the Prophet, peace and blessings be upon him, did not forbid its use but rather approved it. However, it is not permissible to mention it in the Adhan (call to prayer), the Iqamah (second call to prayer), or the Tashahhud (testimony of faith during prayer), because the fundamental principle in acts of worship is adherence to tradition (ittiba'), and this addition was not mentioned in the narrated Prophetic wordings. Adding it does not invalidate the prayer, though it is preferable to adhere to the reported forms.