The idea is that I want a smooth transition without the hole in the splitting region, I’ve tested a few different ways to do the transition, but always get some kind of pinching, a hole, or self-intersecting model.
I’d like to know which one would be the best practice in regards to subd modeling, and if there are any other ways of achieving this.
I would recommend to start with a face-layout, that has a nice stripe / loop of faces (violett) around the cut.
This will give you all necessary control to shape the cut as you like.
And avoids n-gons and star-points at the cut.
(EDIT: new file, minimal update to have nicer top-view)
you can start with Version (5) of your file, and use _subDivide.
Then delete some of the new edges and _slide to get the layout from the screenshot.
… for sure there is may different approaches to get it.