I’ not sure why the actual wording of the coronation oath means I’m going around in circles? You can look it up. That’s exactly what it says.
The wording can be explained by the word spoken by the Archbishop of Canterbury just before Charles took the oath “The Coronation Oath has stood for centuries and is enshrined in law”
What you are so exercised about (three question marks, no less) is semantics. The verb applyied to the function a monarch undertakes will be a choice between government or rule, mostly - that just established usage. As a constitutional monarch, the laws Charles is therefore undertaking to govern in accordance with are those very laws that set out his role as an apolitical figurehead. So there is no inconsistency.