That's not quite what it says.

"A well regulated Militia, being necessary to the security of a free State, the right of the people to keep and bear Arms, shall not be infringed."

1. The reason is well-regulated militias, but the right is of the people.

2. The militia isn't a state apparatus. Indeed, the goal of the militia is to enable a rebellion if the state is no longer free.

Now, here again, "well regulated" gives plenty of leeway. For example, one might argue that the following scheme fits:

1. I can have whatever arms I want, including an F35

2. The F35 lives with a militia, which is well-regulated. I can use it in trainings there.

I don't think one could argue the militia could be under state control (that defeats the purpose!), but one could easily argue that it could be well-enough regulated that the current far-right extremist groups would not fit.

The concept was a group of citizens under e.g. a town / city council.

That's obviously not where case law went, but in an alternative reality, it very well might have.