How did the author of the Book of Psalms know that?

It was written with divine inspiration, no?
But there are earlier sources too. In the Torah itself we are commanded: "You shall do what is upright and good." And in several places the Holy One, blessed be He, says that He will do good to us and condemns evil, and so on.

A. God commands us to do what is upright and good, and you say that the reason of the Merciful One is that the Merciful One Himself is good? Or is it based on the assumption that the Holy One, blessed be He, observes the entire Torah, and just as He puts on tefillin so too He acts according to what is upright and good?

B. When the Torah (and the Hebrew Bible) attributes all kinds of qualities to God, the intention is presumably—or at least it is easy to explain it this way—that He will act in that manner. "And hear, for I am gracious" would mean that if he cries out, then I will treat him graciously. Nowadays, when this apparently does not happen (providence, etc.), then on the face of it the whole verse is not valid for our time. Not that God remains "in Himself" gracious, but rather that new reasons cause Him to stop doing that. Maybe the new reasons were דווקא in the past, and therefore only then did He act graciously?

C. What practical difference does it make whether the Holy One, blessed be He, is good or not? Meaning, in my terms, does the idea of suffering and pleasure interest Him at all?

A. According to both possibilities, it comes out that He is good. But I meant the first one (the assumption underlying the second possibility is merely an aggadic homily).
B. It does happen. Just not through intervention at every moment, but in the very structure of the world.
C. I have no idea. But when He tells us that He is good, apparently suffering and pleasure do matter to Him.

A. If this is on the basis of the reason for the verse, then just as in all other Jewish laws you assume that the reason is some hidden halakhic value, why, with regard to the Jewish law or moral recommendation to do what is upright and good, do you refrain from assuming a hidden halakhic value and slip into an ordinary human reason?
B. It seems pretty clear to me that when the Hebrew Bible describes God as gracious, it means at the very least that God acts graciously. That follows from the contexts, and it also stands to reason that they did not come merely to tell us irrelevant things about the essence of the Holy One, blessed be He. And nowadays that does not happen, as you wrote elsewhere, for the most part. So now one could think either that "in truth He is gracious," but nowadays there are reasons because of which He refrains from graciousness, or that "in truth He is not gracious," but in the past there were reasons because of which He displayed graciousness. And between at least those two interpretations one has to choose the more plausible one. I didn't understand your answer on that.

A. On the contrary, go and see that no enumerator of the commandments counts "You shall do what is upright and good" among the commandments. This is not Jewish law but Torah guidance, that is, morality.
B. He indeed acts graciously. When He creates a world, He makes it in an optimal way. The lack of intervention stems from good reasons, and therefore does not indicate that He is not gracious.

(According to what is described in Genesis, the good precedes God. God does something and then sees that it is indeed very good. Or, "and you shall be like God, knowing good and evil"—from these it would seem that good and evil precede God.)

But why does it matter to God that what He made is good? Presumably otherwise God would not have been pleased with it. And what makes Him good is the fact that He created the world and chose to keep it because what He created turned out good.
In other words, what defines a person as good is that he enjoys good things (and recoils from bad things); a bad person enjoys bad things.

And in this simple sense, God is good.