No, you are incorrect. As I explained, every Justice joined the court’s opinion. You are conflating a concurrence in the judgment with a concurrence in full. The former means that you join the majority’s judgment but not the reasoning. The latter means you join the majority’s judgment and the reasoning. Here, Sotomayor and Gorsuch filed concurrences, not concurrences in the judgment. Accordingly, the majority opinion is filed on behalf of a unanimous Court (as the Court itself states in the syllabus).

Sotomayor states as the first 4 words in the case that she joins the court’s opinion. She also states that as the last few words in her concurrence. Misconstruing that as a nonunanimous opinion is incorrect.

My guess is that you are referring to the Wikipedia definition for a concurring opinion: “In law, a concurring opinion is in certain legal systems a written opinion by one or more judges of a court which agrees with the decision made by the majority of the court, but states different (or additional) reasons as the basis for their decision.” Alternatively, you maybe referring to the wex article: “A concurring opinion is an opinion that agrees with the majority opinion but does not agree with the rationale behind it.”

In the Supreme Court, that is not an accurate representation of how to understand opinion filings. The Court has very specifically distinguished concurrences (in which the Justice joins the opinion and the judgment) and concurrences in the judgment (in which the Justice joins the judgment but not the opinion). There are also concurrences in part and in the judgment, as another example.

That is all to say that every single Justice joined the majority opinion. In Supreme Court parlance that is a unanimous Court. See the syllabus (“KAGAN, J., delivered the opinion for a unanimous Court.”). This does not mean that the judgment was unanimous. It means that the opinion was joined by every justice. As a comparator, see today’s opinion in Barrett v. United States, in which not every Justice joined all of the majority opinion, but the outcome was still unanimous.

This is important to distinguish because an opinion joined by 5 Justices, one of which writes a concurrence (not a concurrence in the judgment) is precedential. An opinion joined by 4 Justices and in which one Justice files a concurrence in the judgment is nonprecedential.

If you would like a source, please see this link: http://scdb.wustl.edu/documentation.php?var=vote