I do not see how my question was even answered...
Your question was "
How does God punish a New Covenant believer? What does that look like today?"
I believe God punishes His children for a reason. To bring them back to Him, just like He has done from the beginning of time. That I why I referenced history. When the "new covenant" believer, whatever that is, steps out of line they are punished to bring them back, just like the prodigal son, whose punishment was wasting all his money and having to eat with the pigs, but thank God he never leaves us nor forsakes us because the voice of the Holy Spirit worked on the prodigal's heart and convicted him to return to his father. If that does not give you an idea of how God punishes His children perhaps you might want to listen to the Holy Spirit in your life. I do not mean any offense by this, but God sent the comforter, and His job is found in John:16:7&8: "Nevertheless I tell you the truth; It is expedient for you that I go away: for if I go not away, the Comforter will not come unto you; but if I depart, I will send him unto you. And when he is come, he will reprove the world of sin, and of righteousness, and of judgment:" When we listen to the Holy Spirit we are convicted, or blessed, or even judged. Have you ever been convicted of your sins? I can answer that whether you admit it or not, the ONLY way one comes to God is because HE calls us. God seeks us we do not, because of sinful nature, seek Him
I hope that answers it.