Is David prideful, deluded, or something else in making these claims?

He, after all, has not always made the best choices.

It must be something else – the same something else available to us: a heart known by God, bathed in mercy, covered by grace, seen through the eyes of love, and living in a constancy of repentance, reorientation, and direction toward God, flawed, forgiven, rebounding, resilient.

He is a fully integrated human with a singular, though imperfect heart for God. His life is oriented around an enduring center.

That is the nature of integrity.

"Vindicate me, O LORD,
for I have walked in my integrity,
and I have trusted in the LORD without wavering.
Prove me, O LORD, and try me;
test my heart and my mind.
For your steadfast love is before my eyes,
and I walk in your faithfulness."