I don’t want to sound to harsh but… I hadn’t seen such a bad pattern in a long time, this is the kind of things that don’t have a name for a good reason. And let me tell you why.
1.- now your method became state aware, if you call them in the wrong order it will not work, but, the wrist part is that there is no way to state that in the method signature.
2.- this is the opposite of what DI wants to achieve, instead of exposing your dependencies, your hide them inside a God object that knows about everything you should ever need. In order to test this type of code you need to know which fields are really accessed from the method, and the only thing telling you that you missed one is a test not passing, those should be at compile time, or even better trough static analysis.
3.- good luck ramping up the new guy, now he needs to learn all that hidden logic that can’t be expressed trough code, just because you wanted to be able to called in a functional programming way.
Let me know if I’m missing something, but, from what I read this were the point that stood out, and for that reason I think this should be an anti pattern.
Again, I have nothing against you and just want to give my constructive feedback.