Squares and rectangles, you can’t generalize a subset as synonymous with its superset.
Congress should establish a requirement that every American be trained on safe handling procedures, as well as on the laws governing the use of force in self defense and defense of others.
You won’t hear any argument from me on this point, I do believe the states should organize and train adults with some degree of competency, although this was written when Militias were the primary national defense in lieu of the standing Army we now maintain.
But the rest of your interpretation reads more like you’re working backwards from the conclusion you want to prove.
Do the states not have the authority to appoint officers over you, or train you according to the discipline prescribed by Congress?
Can you not be called forth to enforce law, suppress insurrection, or repel invasion?
Broadly speaking, no I would not say that’s the case .
The founders did not make a habit of codifying lazy verbage, if they meant People in general they would have written People in general. They chose the words they did to convey specific and distinct meanings. Militia refers particularly to that portion of a community trained for “martial exercise”. If you’re not trained, I’d argue specifically trained by the state, you’re not part of the Militia. A candidate for it perhaps, but not a member until you’ve been trained by the state for the purpose.