I've been working over 1Samuel 15 and because I seem to not get to the heart of your question, I thought perhaps SV commentary could enlighten the perspective and help flesh-out the SV perspective and help us sort out the thoughts. If you have an OV commentary portion for this, I think it would help us both look very objectively. We can analyze what others are saying, see why they don't address the concerns respectively etc.
John Gill (Baptist): "1Sa 15:11 - It repenteth me that I have set up Saul to be king,.... Which is not to be understood of any change of mind, counsel, purpose, or decree in God, which is not consistent with his unchangeable nature; but of a change of dispensation, and outward dealings, and is spoken after the manner of men, who, when they repent of anything, change the course of their conduct and behaviour; and so the Lord does without any change of his mind and will, which alters not; and though he changes the outward dispensations of his providence, yet he never changes and alters in the matters and methods of his grace; though he repented he made Saul king, he never repents of his making his saints kings and priests for himself; his outward gifts he sometimes takes away, as an earthly crown and kingdom; but his gifts and calling, which are of special grace, are without repentance."
From the Armenian view: John Wesley: "1Sa 15:11 - Repenteth - Repentance implies grief of heart, and change of counsels, and therefore cannot be in God: but it is ascribed to God when God alters his method of dealing, and treats a person as if be did indeed repent of the kindness he had shewed him. All night - To implore his pardoning mercy for Saul, and for the people. Is turned back - Therefore he did once follow God. Otherwise it would have been impossible, he should turn back from following him. 1Sa 15:29 - Strength of Israel - So he calls God here, to shew the reason why God neither will nor can lie; because lying proceeds from the sense of a man's weakness, who cannot many times accomplish his design without lying and dissimulation; therefore many princes have used it for this very reason. But God needs no such artifices; he can do whatsoever he pleaseth by his absolute power. Repent - That is, nor change his counsel; which also is an effect of weakness and imperfection, either of wisdom or power. So that this word is not here used in the sense it commonly is when applied to God, as in Jer. 11:1-23, and lsewhere."
Kiel & Deilitzsch (Lutheran with Calvin influence): 1Sa 15:10-11 - The word of the Lord came to Samuel: “It repenteth me that I have made Saul king, for he hath turned away from me, and not set up (carried out) my word.” (On the repentance of God, see the remarks on Gen_6:6.) That this does not express any changeableness in the divine nature, but simply the sorrow of the divine love at the rebellion of sinners, is evident enough from 1Sa_15:29.
1Sa_15:29 : “And also the Trust of Israel doth not lie and doth not repent, for He is not a man to repent.” נצח signifies constancy, endurance, then confidence, trust, because a man can trust in what is constant. This meaning is to be retained here, where the word is used as a name for God, and not the meaning gloria, which is taken in 1Ch_29:11 from the Aramaean usage of speech, and would be altogether unsuitable here, where the context suggests the idea of unchangeableness. For a man's repentance or regret arises from his changeableness, from the fluctuations in his desires and actions. This is never the case with God; consequently He is ישׂראל נצח, the unchangeable One, in whom Israel can trust, since He does not lie or deceive, or repent of His purposes. These words are spoken θεοπρεπῶς (theomorphically), whereas in 1Sa_15:11 and other passages, which speak of God as repenting, the words are to be understood ἀνθρωποπαθῶς (anthropomorphically; cf. Num_23:19).
He was 'seen to sigh' (2 Hebrew words "seen" "sigh") which is translated 'repent' ( "and God 'made known His sigh").