Why does the Gospel of John say its signs were written down?

Answer: So that you may believe

John 20:31: "These are written so that you may believe that Jesus is the Christ, the Son of God," and by believing have life.

“Jesus performed many other signs in the presence of His disciples, which are not written in this book. But these are written so that you may believe that Jesus is the Christ, the Son of God, and that by believing you may have life in His name.”— John 20:30-31 (BSB)