Well, magical or not because “Officers of the United States” must be appointed by the President “by and with the Advice and Consent of the Senate.” U. S. Const., Art. II, §2, cl. 2. it is the law that assigns and separates the powers between the branchs.
That general rule is subject to one Constitutional exception: “The President shall have Power to fill up all Vacancies that may happen during the Recess of the Senate, by granting Commissions which shall expire at the End of their next Session.” Id., §2, cl. 3.
All these words and their original and formal meaning are not in dispute. To be sure, we use words such as "recess" colloquially but the Constitution has a formal 18th century meaning.
There are 'Sessons' and "the Recess" (not "a recess" but "the Recess". They are distinctly different. Congress meets twice a year in "Sessions" and the period in between is "the Recess". This distinction exists to prevent the President from nullifying the Senates Constitutional role and power in the appointment process during a simple break or adjournment. It recognizes that there is a lengthily gap between Sessions of Congress, for which the President might critically need the advice and assistance of an official. And if there is a vacancy "that happens" in that period the exception applies.
The 10 day rule is solely an invention of modern courts, and not even a logical one. The whole point of the Constitutional clause is to cover was used to be a very long period between sessions. It was not made to address something as brief as 10 days because there is NO reason to rush through a vacancy and avoid the confirmation process because the Senate doesn't meet for a 10 day period. Perhaps a 30, 60, or 90 day rule but not one that allows a President a way to ignore the right to confirm.