Expanding the court doesn't require congressional approval
That is incorrect. Changing the size of the Court is understood to be a power that Congress has because of the Necessary and Proper clause, and not a power of the Executive.
For an act changing the size of the Court to pass the Senate, you first need 60 Senators to break the filibuster. This means that 10 Republican Senators need to vote for increasing the size of the Court for any such legislation to pass. That’s not going to happen.
Biden could not have expanded the court. That requires an act of Congress. Even if the Democrats passed such an act in the House, it would have been dead in the Senate because they have never had the needed supermajority and none of the Republicans would have voted for it.