Whilst what you would like to do is partly possible, constraints are purely 2D and they only become 3D by association with for example the extrude tool, even though it looks like 3D its still only constrained by the 2D profile.
Although it is possible to partly constrain the holes in your drawing, it won't be fully constrained as changing the height of the extrude will not be reflected in the position of the holes, to do it partly constrained, one would set up a constrains on a workplane on the side of the object, BUT its still hit and miss, and one needs (or at least I did) setting up everything before joining the side constraints to the bottom ones using equal length or the constraints break.
I don't think constraints were ever designed for this type of adjustment. and apart from 3 extra tool, they haven't really changed much since introduction in v10.5. If your used to a fully parametric program where you can change everything and have the change reflect on other sizes / faces in all directions, I'm doubt constraints would do it, maybe the parametric parts in TC could do it, but I know nothing about programming parametric parts.
attached is the closest I got, and is animated by changing 3 variables, note I used a circle point object rather than a star - just because I think it looks clearer.