They don’t need amendments to the constitution to adjust the supreme court, only laws, as long as those laws don’t conflict with what is written in the constitution. For instance, the reason we have nine justices and not eight or ten, is because of a law passed by congress. So congress can change that anytime it feels like. The number of justices is not set in the constitution. There’s actually very few details about the supreme court in the constitution, so congress has a lot of latitude to regulate and make changes to the supreme court.
One thing that’s popular that would likely require a constitutional amendment though is term limits for justices, because the lifetime appointment is a detail specified in the constitution. So basically, congress regulates and sets up the court system through passed laws, most changes to the court system including to the supreme court don’t need constitutional ammendments. Alito is talking out of his ass when he says congress can’t do this.
Unfortunately Congress’s only real recourse if the supreme court declares themself above the law and ignores congress like Alito wants them to, would be for congress to get off its butt and impeach some justices, which seems very unlikely. I would hope Roberts and at least one other would want to avoid a constitutional crisis though that would risk a total collapse of supreme court authority, but I’m not sure. The corruption seems to run deep with a number of them.