Constrains using null space in dolfinx

Unfortunately, I cannot reproduce this behaviour.

You are using the wrong form.
You should use dolfinx.fem.form, not ufl.form.
Remove form from

You have a function space V that is a vector function space.
The input to interpolate is a set of coordinates, x, of shape (3, number_of_points), where x[0] is the list of all x-coordinates, x[1] all y coordinates etc.
The input is designed this way so that you can used vectorized functions in numpy.
As your space is a vector space of dim=3, the output should be (3, number_of_points), not just number_of_points.

Not sure why you would want such a constraint, what is the physical interpretation of this.

This is a topic covered in many other posts on discourse, see for instance: Periodic BC in dolfinx - #2 by nate