I don't know the connection between the four points, but it may help to redefine holonomy in your first point. A constraint is generally a regular distribution (in the sense of a subbundle of the tangent bundle of the configuration manifold).
If that distribution is integrable, then the constraint is said to be holonomic. And indeed, by restricting the system to one particular integral submanifold, one obtains the definition of holonomy in your first point.
The point is, in mechanics, "holonomic" is just another word for "integrable distribution". If the constraint distribution is not integrable, the system is called "nonholonomic".
Maybe that may help to make a connection with point 4.?
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