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.
You are effectively implying this, but I will say it explicitly - you don’t need immunity to reconcile the logical conflict. The courts can simply find that that law is unconstitutional facially (if it is specifically directed at an enumerated executive power) or as-applied (if it is a general law that sweeps in executive conduct that falls under an enumerated power). In other words, it’s not that the President is immune from criminal prosecution for violating a criminal statute, but instead Congress violated the separation of powers when passing the law and it therefore can’t be enforced because it is unconstitutional. In that situation, this would be a defense to the prosecution, with the burden being on the President to raise and prove the unconstitutionality of the law just like any other defendant. We don’t need to invent a new immunity to protect the President against Legislative excesses.