I can understand why piping is attractive, and if you want it as a language defining feature as the author that's your prerogative. :)

So is the .new() method in that case an alternate constructor (i.e. constructor code will not run only the contents of the new method will) or is it a method being invoked after the constructor code runs?

No, there's only one constructor for any given class. The body of a class is the constructor of a class, and that constructor is made available through a method called .new. It's sort of like...Python, and imagining that you get __init__ created for you automatically. It's just two ways of doing the same inner call.

Python omits the new() thing, didn't miss it yet.

An alternative would be Uniform Function Call Syntax: https://dlang.org/spec/function.html#pseudo-member