The Justices themselves would beg to differ, as they are currently riding the doctrine of originalism, which places great importance on works such as the Federalist Papers and other extemporaneous documents.
But, just for fun.
Lets step back from originalism and proceed under the textualist approach, which I favor as a first approach anyhow, with originalism being secondary if nexcessary.
Textually speaking.
The term public ministers occurs four times in the Constitution, twice in Article II and twice in Article III. It does not appear in any of the amendments.
I will give those occurrences, in the full context of their occurrences.
From Article II:
Section. 2. The President shall be Commander in Chief of the Army and Navy of the United States, and of the Militia of the several States, when called into the actual Service of the United States; he may require the Opinion, in writing, of the principal Officer in each of the executive Departments, upon any Subject relating to the Duties of their respective Offices, and he shall have Power to grant Reprieves and Pardons for Offences against the United States, except in Cases of Impeachment.
He shall have Power, by and with the Advice and Consent of the Senate, to make Treaties, provided two thirds of the Senators present concur; and he shall nominate, and by and with the Advice and Consent of the Senate, shall appoint Ambassadors, other public Ministers and Consuls, Judges of the supreme Court, and all other Officers of the United States, whose Appointments are not herein otherwise provided for, and which shall be established by Law: but the Congress may by Law vest the Appointment of such inferior Officers, as they think proper, in the President alone, in the Courts of Law, or in the Heads of Departments.
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.
Section. 3. He shall from time to time give to the Congress Information of the State of the Union, and recommend to their Consideration such Measures as he shall judge necessary and expedient; he may, on extraordinary Occasions, convene both Houses, or either of them, and in Case of Disagreement between them, with Respect to the Time of Adjournment, he may adjourn them to such Time as he shall think proper; he shall receive Ambassadors and other public Ministers; he shall take Care that the Laws be faithfully executed, and shall Commission all the Officers of the United States.
From Article III:
Section. 2. The judicial Power shall extend to all Cases, in Law and Equity, arising under this Constitution, the Laws of the United States, and Treaties made, or which shall be made, under their Authority; — to all Cases affecting Ambassadors, other public Ministers and Consuls; — to all Cases of admiralty and maritime Jurisdiction; — to Controversies to which the United States shall be a Party; — to Controversies between two or more States; — between a State and Citizens of another State [Modified by Amendment XI]; — between Citizens of different States; — between Citizens of the same State claiming Lands under Grants of different States, and between a State, or the Citizens thereof, and foreign States, Citizens or Subjects.
In all Cases affecting Ambassadors, other public Ministers and Consuls, and those in which a State shall be Party, the supreme Court shall have original Jurisdiction. In all the other Cases before mentioned, the supreme Court shall have appellate Jurisdiction, both as to Law and Fact, with such Exceptions, and under such Regulations as the Congress shall make.
In three of the four occurrences, it occurs in the context of ambassadors, other public ministers and consuls. In one occurrence, it occurs in the context of ambassadors and other public ministers.
It is the occurrences in Article II that are most telling. In the appointment clause in Section 2 of Article II, Ambassadors, public ministers and consuls are pointedly grouped together, followed by Judges of the Supreme Court, followed by all other Officers of the United States, a term which includes not only officers in the executive branch, but all lower court judges. Officers of the United States is a vastly encompassing term but does NOT include ambassadors, public ministers and consuls as these officers are diplomatic in nature.
Later in Section 3 of Article II, it is stated that the President shall receive ambassadors and other public ministers. The Constitution exclusively vests the diplomatic function in the President and public ministers clearly is meant to refer to foreign diplomatic officers.
As you can see, a textualist approach makes the same ironclad case that an originalist approach does.
Public ministers refers exclusively to diplomatic officers.