Want to change size of SCOTUS? You need Congress to pass a law.
Want to seat someone on SCOTUS? You need Senate confirmation.

GOP holds ace in the hole with 48/50/2 split and no way to end filibuster on changing the rules so long as Manchin and Sinema are against changing the rules. You know damned well GOP will do so moment they have a chance, because it would leave Democrats in a permanent disadvantage as the GOP agenda gets supercharged.

There are no executive actions Biden can take to address the Court. None.

Can he make statements indicating support for expanding the Court? Sure. Can he pressure Manchin and Sinema to go along with court expansion? Yeah. Will those two listen?

Nope.

There’s value signaling and benefit to Biden going out and saying, we intend to expand the court to match the number of circuits. There’s benefit of saying that we intend to change how the Court is comprised. There’s a political one and a party one. It shows you intend to do something. You’re signaling to the base that you intend to fight on multiple fronts.

But what Biden can actually do is quite limited here. Separation of powers and all - and Congress holds the cards - they write the laws setting the Court’s composition and jurisdiction.