DOC/API: Move Styler import (#16059)

* DOC/API: Move Styler import

From the top-level to pandas.io.formats.style.Styler, which is a bit wordy
but I was having circular-import issues at pandas.io.formats.
I think that's ok since people won't really be using this interactively.

Closes #16009

* Added deprecation warning and shim

Author: TomAugspurger