Since I'm a reasonably well-known textualist, I'll bite:
First, the court was not asked to reconsider the meaning of the First Amendment. In the US, we generally hew to the rule of "party presentation," which generally provides that courts will consider the parties' arguments, not make up new ones on their own.
TikTok's claim was that application of the statute in question to it violated the First Amendment's clause that "Congress shall make no law...abridging the freedom of speech." The Supreme Court has considered the interpretation and application of that clause in...well, a whole lot of cases. TikTok asked the court to apply the logic of certain of those precedents to rule in its favor and enjoin the statute. It did not, however, ask the court to reconsider those precedents or interpret the First Amendment anew.
Since the court was not asked to do so, it's no surprise that it didn't.
Second, as noted, the court has literally decades' worth of cases fleshing out the meaning of this clause and applying it in particular circumstances. Every textualist, so far as I'm aware, generally supports following the court's existing precedents interpreting the Constitution unless and until they are overruled.
Third, even if one is of the view that the Court ought to consider the text anew in every case, without deferring to its prior rulings interpreting the text, this would have been a particularly inappropriate case for it to do so. A party seeking an injunction, as TikTok was, has to show a strong likelihood of success on the merits. That generally entails showing that you win under existing precedent. A court's expedited consideration of a request for preliminary relief is not an appropriate time to broach a new theory of what the law requires. The court doesn't have the time to give it the consideration required, and asking the court to abrogate its precedents is inconsistent with the standard for a preliminary injunction, which contemplates only a preview of the ultimate legal question, not a full-blown resolution of it.
Fourth, what exactly was the court supposed to do with the text in question, which is "abridging the freedom of speech"? The question here is whether the statute here, as applied to TikTok, violates that text. Well, it depends on what "the freedom of speech" means and perhaps what "abridging" means. It's only natural that a court would look to precedent in answering the question. Precedent develops over time, fleshing out (or "liquidating," to use Madison's term) the meaning and application of ambiguous or general language. Absent some compelling argument that precedent got the meaning wrong, that sort of case-by-case development of the law is how our courts have always functioned--and may be, according to some scholars, itself a requirement of originalism.