Sigh ...
Congratulations to you for your "big words."
Stare decisis (Latin for "the decision stands") is indeed a short hand way of expressing the principle that courts should follow case law precedent. It is "binding" precedent when the prior court opinion is from a higher court within the same state, circuit or (in the case of the U.S. Supreme Court) country. Otherwise, it is "persuasive authority" (i.e., non-binding precedent).
One thing you overlooked, however, is that a prior court opinion has precedential value only to the extent that the facts of the prior case are similar to those of the case under consideration. If a case has very similar (verging on the same) set of facts, it is said to be "on all fours with" the case under consideration.
You cited
Dred Scott v. Sanford as form of precedent for the birthright citizenship case currently pending in the U.S. Supreme Court, noting (correctly) that its holding (that black slaves were not U.S. citizens even though born in this country) gave impetus to the adoption of the 14th Amendment. But, unfortunately for you, nothing in the 14th Amendment states that its effect is limited to former slaves. Its phraseology is far more general than that.
If you wanted to cite a case which is much closer to being on all fours with the current birthright citizenship case, you would have cited the U.S. Supreme Court case of
United States v. Wong Kim Ark 169 U.S. 649 (1898), in which the Court held that birthright citizenship is guaranteed by the 14th Amendment for children born in the U.S. to foreign-born parents, upholding
jus soli (citizenship by birth). This ruling confirmed that nearly all children born on U.S. soil are citizens, regardless of their parents' status. THAT is the case that the current Supreme Court will need to either overrule or somehow distinguish if it decides to limit birthright citizenship.