The primary viewpoint is that the following section, Proverbs 24:23f, is from a different source. This is because one of the major views is that Proverbs is not as unified as, say, Ecclesiastes, and has material from multiple sources with no real cohesion.
I don’t buy that theory, however well-regarded it may be. I think Proverbs presents as being compiled at the hand or command of Solomon. The final version is, for the most part, Solomonic in construction. I know Proverbs 25:1 references Hezekiah, but even this reference gives credit to Solomon as the author.
I think what we see in Proverbs 24:23 is not a simple editorial note. It is a marker of importance. Here’s what I mean:
Throughout Proverbs, you have multiple statements about “listen to your father, listen to your mother.” You have other statements about “teachers” and designated “advisers.” Specific guidance is highlighted by pointing out who else supports it.
Likewise here. The sayings that follow about judgments and justice are commended to the sons of Solomon because it’s not only Dad’s advice, it is well-known sayings of the wise. The sayings are valuable and framed with a parental “Don’t just take my word for it, listen to others!”
Because this information is about working in areas of judgment and justice. There are aspects of Proverbs that reflect on living life in general and aspects about being the king. The former was personal, the latter would only apply to one. All of the royal family, though, could expect to sit in judgment of cases. It was not uncommon, though sometimes it was trouble for the one on the throne.
Keep in mind that Solomon must not only prepare one son for the throne (the ill-fated Rehoboam) but prepare all of his other sons for their future duties. Proverbs is not targeted only at Rehoboam, for if it was, it was surely a failure given his spectacular flame-out as king. If we see Solomon as providing wisdom for all of his sons, though, we see a better statement about the Proverbs in general.
The following sayings, then, are not just what matter to kings. They matter to all the wise. Including us, if we would be wise. What does Solomon start off with here?
To show partiality in judgment is not good.
Want to grasp that? Genesis 1 is the place to turn. What God does? Good. If you are trying to be godly in your behavior, act on the things of God, guide the people of God, then “good” is your standard, because God is your standard. (Mark 10:8)
If it’s not good, then it’s not of God. So don’t do it.