As selamu aleykum.In the seyyidul istighfar dua,are the wa'ad and the ahd mentioned, referring to the promise we made to Allah when he created our souls that He was our lord and we would not worship anyone or thing besides him or does it refer to something else? Jazaakumullahu khayr.

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.

The meaning which you referred to in the question is the same meaning pointed to by some commentators on Hadeeth. Ibn Battaal when commenting on the Hadeeth of Sayyid al-Istighfaar (the master supplication for forgiveness) in Saheeh Al-Bukhari (which reads: O Allaah You are my Lord. None has the right to be worshipped but You. You created me and I am Your slave, and I am faithful to Your covenant and my promise to You as much as I can. I seek refuge with You from all the evil I have done. I acknowledge before You all the blessings You have bestowed upon me and I confess to You all my sins. So, forgive me, for nobody can forgive sins except You.) said: “It means: the covenant that Allaah took from His slaves when He created them and brought them out from the loins of their fathers like atoms and He made them to witness as to themselves (saying to them) {… “Am I not your Lord?” They said, “Yes, we have testified.”}[Quran 7:172] So, they testified when they were created that Allaah is their Lord, and they submitted themselves to Him as the One and Unique Lord. As regards the promise, it is: What Allaah promised them, that whoever dies and does not associate anyone or anything with Allaah and did what Allaah ordained him to do, that he will enter Paradise. So, each Muslim should supplicate Allaah to make him die on that covenant and on ‘Eemaan (faith), so that he would achieve what Allaah has promised the one who fulfills this, and as a way of imitating the Prophet in his supplication (in this regard).”

Thus, it is clear that Ibn Battaal distinguished between the covenant and the promise and he interpreted the promise to be Allaah's promise of reward.

Nevertheless, some commentators interpreted the covenant with the same meaning of promise. For example, As-San’aani said in his book "Subul As-Salaam": “Its meaning according to Al-Khattaabi is: I am on the covenant which I made with You and the promise which I gave to You to have faith (‘Eemaan) in You, and to devote my entire acts of obedience to You as much as I can while holding fast to it, and I ask You to fulfill Your promise of reward and compensation.”

Allaah Knows best.