What is the most complete formula for sending prayers and salutations upon the Prophet, may Allah’s peace and blessings be upon him, together, especially since the Ibrahimiyyah formula does not include salutations upon him? And is it permissible to add "Peace be upon you, O Prophet, and Allah's mercy and blessings" before or after the Ibrahimiyyah formula?

It is not obligatory to combine the prayer (ṣalāt) and the salutation (salām) upon the Prophet, peace and blessings be upon him. Rather, it is permissible to say each one individually, as there are aḥādīth that indicate this. The Companions knew how to greet him even before the command to pray upon him was revealed. When the verse was revealed, they asked him about the manner of prayer, and he replied: "SAY: O ALLAH, PRAY UPON MUHAMMAD... AND THE SALUTATION IS AS YOU HAVE ALREADY LEARNED." The most complete form is to combine them both. The matter is broad in this regard, but what is established in the āthār (narrations) is more preferable and carries greater reward.