What can we learn from King Solomon if he possibly missed the mark?

To me, it would be a profound irony and tragedy—if one of the wisest men in history (1 Kings 3:12; 4:29–31), famed for building the temple (1 Kings 5–6) and writing Proverbs and Ecclesiastes, a foreshadowing type for Jesus (Matthew 12:42), yet potentially missing out on the Kingdom. One of his last mentioned acts is trying to kill Jeroboam (1 Kings 11:40; Exodus 20:13) before his death and burial is shortly described next in 1 Kings 11:42-43. This raises doubtful concern for me, about his standing in terms of salvation (Ezekiel 18:24; 1 Corinthians 9:27) or if counted among the “Hall of Faith” in Hebrews 11. Albeit, not denying the possibility of him yielding to God's profound transformative power and healing over his faith walk in the last parts of his life (Psalm 103:8–12; 136; 145:8-18). "Solomon tried to kill Jeroboam, but he fled to King Shishak of Egypt and stayed there until Solomon died. The rest of the events in Solomon’s reign, including all his deeds and his wisdom, are recorded in Solomon ruled in Jerusalem over all Israel for forty years. When he died, he was buried in the City of David, named for his father. Then his son Rehoboam became the next king." Given that Scripture never clearly affirms or denies Solomon’s salvation, and considering his extraordinary wisdom and accomplishments (1 Kings 11:41), what does his life reveal about the relationship between human achievement, divine judgment, and authentic or saving faith in God (Ecclesiastes 1:16–17, 2:4–9; Hebrews 11)?