Previously the Fifth Circuit had relied heavily on Ginsberg v. New York (1968) to justify rational basis review. But Ginsberg was a narrow scope - it held that minors don't have the same First Amendment rights as adults to access "obscene as to minors" material. It wasn't about burdens on adults at all. Later precedent (Ashcroft, Sable, Reno, Playboy) consistently applied strict scrutiny when laws burdened adults' access to protected speech, even when aimed at protecting minors.
In Paxton the majority split the difference and applied intermediate scrutiny - a lower bar than strict - claiming the burden on adults is merely "incidental." Kagan had a dissent worth reading, arguing this departs from precedent even if the majority won't frame it that way. You could call it "overturning" or "distinguishing" depending on how charitable you're feeling.
The oral arguments are worth watching if you want to understand how to grapple with these questions: https://www.youtube.com/watch?v=ckoCJthJEqQ
On 1A: The core concern isn't that age-gating exists - it's that mandatory identification to access legal speech creates chilling effects and surveillance risks that don't exist when you flash an ID at a liquor store.
Note: IANAL but do enjoy reading many SC transcripts