Tzedek is usually handed to us as "righteousness," and by the time KJV, ESV, NASB and NIV are finished with it in Romans the word has become a legal status, something declared over you in a heavenly courtroom while you yourself stay exactly as you were. That is not what the Hebrew is doing.

The root carries the sense of straightness, of a thing conforming to the standard it was made for. A tzedek weight is an honest weight, one that actually weighs what it claims to weigh (Deuteronomy 25:15). Righteousness in Hebrew is less a verdict and more a shape.

Watch what David does with it in Psalm 119. "Righteous are you, YHWH, and upright are your judgments" (119:137). "Your righteousness is righteous forever, and your Torah is truth" (119:142). He lays tzedek directly on top of the Torah, as though they were two names for one thing, because to him they were. The instruction is the shape. Righteousness is a life pressed into it.

Carry that back into Sha'ul and the courtroom drains out of the word. The righteousness of God is HaShem setting things right, making whole what was bent, and finally writing the instruction where it can actually be walked.