Your understanding is flawed, - as can be read. -- I'll highlight the points where state officials & offices are mentioned:
"-- This Constitution, and the Laws of the United States which shall be made in Pursuance thereof; and all Treaties made, or which shall be made, under the Authority of the United States, shall be the supreme Law of the Land; and the Judges in every State shall be bound thereby, any Thing in the Constitution or Laws of any state to the Contrary notwithstanding.
The Senators and Representatives before mentioned, and the Members of the several State Legislatures, and all executive and judicial Officers, both of the United States and of the several States, shall be bound by Oath or Affirmation, to support this Constitution; but no religious Test shall ever be required as a Qualification to any Office or public Trust under the United States. --"
Thus, all 'offices or public trusts' are under [subject to] the [constitution of] the United States.
In fact, even ordinary people are subject to abusing our Constitution if acting under color of law:
"-- Title 18, U.S.C., Section 242 Deprivation of Rights Under Color of Law
This statute makes it a crime for any person acting under color of law, statute, ordinance, regulation, or custom to willfully deprive or cause to be deprived from any person those rights, privileges, or immunities secured or protected by the Constitution and laws of the U.S. Acts under "color of any law" include acts not only done by federal, state, or local officials within the bounds or limits of their lawful authority, but also acts done without and beyond the bounds of their lawful authority; provided that, in order for unlawful acts of any official to be done under "color of any law," the unlawful acts must be done while such official is purporting or pretending to act in the performance of his/her official duties.
This definition includes, in addition to law enforcement officials, individuals such as Mayors, Council persons, Judges, Nursing Home Proprietors, Security Guards, etc., persons who are bound by laws, statutes ordinances, or customs. --"
I stated correctly that the original Constitution did not set conditions for state and local offices. When you cite Title 18 as setting such conditions maybe 200 years later, you certainly prove me right that it wasn’t in the original Constitution.