There isn’t an actual Halacha derived. It mentions a Psak in the story. That is not the same thing.
For example, the Gemara discusses distances on earth in relation to the Zmanim. We know they meant it in the full meaning of the word since they are discussing practical ramifications. However, in this case, Chazal hadn’t derived anything practical from the story.
In fact, we don’t ‘Pasken‘ like any of Shlomo Hamelech’s trick Psakim. We can’t use motherly love, as proof of parenthood, in a Beis Din. Shlomo Hamelech saw the whole situation, it might have included Ruach Hakodesh, and being an undecidable case it might have allowed for Shuda deDayne—assumption of the judge.