In that action, he prefigured Christ. His psalms also prefigure Christ, and Our Lord quoted them.
You wrote (regarding things someone else said of David):All of that is true, while still omitting so much.
"Prophet" is one of the things omitted.
There is, of course, this:
Acts 2:
25 For David saith concerning him: I foresaw the Lord before my face: because he is at my right hand, that I may not be moved. 26 For this my heart hath been glad, and my tongue hath rejoiced: moreover my flesh also shall rest in hope. 27 Because thou wilt not leave my soul in hell, nor suffer thy Holy One to see corruption. 28 Thou hast made known to me the ways of life: thou shalt make me full of joy with thy countenance. 29 Ye men, brethren, let me freely speak to you of the patriarch David; that he died, and was buried; and his sepulchre is with us to this present day. 30 Whereas therefore he was a prophet, and knew that God hath sworn to him with an oath, that of the fruit of his loins one should sit upon his throne. 31 Foreseeing this, he spoke of the resurrection of Christ. For neither was he left in hell, neither did his flesh see corruption. 32 This Jesus hath God raised again, whereof all we are witnesses.
Thanks.