As I see it, it's crucial to acknowledge the source of the maxim - from inscriptions on the Temple of Apollo at Delphi where this was 1st of 3 above the entrance, so held in the highest honour of all. Delphi, where prophecies considered of the highest significance, including by Socrates, were given for around 900 years, among the longest continuously practicing religious institutions.
As the story of Socrates shows, prophecies aren't neutral things and frequently are ambiguous; a person brings who they are to a prophecy, how they will respond is part of it - just as more usually in tragic terms, like the prophecy on Oedipus. Socrates brought his wisdom to being called the wisest in Athens, by making his response a parable on how to practice wisdom & humility.
Wisdom has fallen out of favour in philosophy, but was a central concern to the Ancient Greeks. I discuss why this change, and how to think about what wisdom is, here: Wisdom and John Vervaeke's awakening from the meaning crises? My summary is that it's about balancing our different selves, what we want now and what we will want in the future, who we are in different contexts, &c. My phrase is that, wisdom involves finding and acting from the integrated centre of our concerns.
Consider also the central role of hubris, and hamartia or the 'fatal flaw' in Greek tragedy. See discussion here: What's wrong with "playing god"? To know yourself also means knowing your limits, staying humble even if you really are the wisest man in Athens: "I seem, then, in just this little thing to be wiser than this man at any rate, that what I do not know I do not think I know either" That too is wisdom.
A prophecy is a blessing on the wise, and a curse on the unwise, because whatever we know about the future, the important thing is that we bring who we are to that knowledge, to that future. By doing the work of, actively practicing knowledge of the integrated centre of our concerns, we can learn not to fight ourselves, or act with excess that we will regret when our mood changes.
I would also relate this picture to the Strange Loop idea of the self, that 'self consciousness' is the capacity to hold a self-model in mind while thinking about possible futures, and using this to decide how to be. This can link a picture of why we have intentions & affective states (to cultivate typical expected outcomes), with multiple selves in relation to 'ptophecied' or expected futures. Knowing what we know about the future, who should you be? That, is knowing thyself. That is the root-koan of Zen: 'Who am I?', meaning how do you bring to bear self meeting world, into this very moment right Now.