DOC/API: Move Styler import

[TomAugspurger]

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

[jorisvandenbossche]

api.rst also needs an update

[jorisvandenbossche]

In this issue (#16009), I also raised the question whether we should deprecate the old location. But is there currently a reason that a user would use the actual object instead of access it through df.style ? (if not, the deprecation is probably not needed?)

[codecov]

Codecov Report

Merging #16059 into master will increase coverage by 0.02%.
The diff coverage is n/a.

@@            Coverage Diff             @@
##           master   #16059      +/-   ##
==========================================
+ Coverage   90.79%   90.82%   +0.02%     
==========================================
  Files         156      155       -1     
  Lines       50534    50518      -16     
==========================================
- Hits        45883    45881       -2     
+ Misses       4651     4637      -14

Flag	Coverage Δ
#multiple	88.59% <ø> (+0.02%)	⬆️
#single	40.45% <ø> (ø)	⬆️

Impacted Files	Coverage Δ
pandas/io/api.py	100% <ø> (+28.57%)	⬆️

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[TomAugspurger]

I believe api.rst was already changed as part of the move.

Style
-----
.. currentmodule:: pandas.io.formats.style

``Styler`` objects are returned by :attr:`pandas.DataFrame.style`.

For the deprecation... I could go either way. 5516aa4 adds a compatibility shim pointing to the new location. I'll add it to the master list if we decide to include it.

[codecov]

Codecov Report

Merging #16059 into master will increase coverage by 0.02%.
The diff coverage is 100%.

@@            Coverage Diff             @@
##           master   #16059      +/-   ##
==========================================
+ Coverage   90.79%   90.81%   +0.02%     
==========================================
  Files         156      156              
  Lines       50534    50521      -13     
==========================================
  Hits        45883    45883              
+ Misses       4651     4638      -13

Flag	Coverage Δ
#multiple	88.58% <100%> (+0.02%)	⬆️
#single	40.45% <0%> (ø)	⬆️

Impacted Files	Coverage Δ
pandas/io/api.py	100% <ø> (+28.57%)	⬆️
pandas/formats/style.py	100% <100%> (ø)
pandas/core/common.py	90.68% <0%> (-0.35%)	⬇️

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[jorisvandenbossche]

I believe api.rst was already changed as part of the move.

Ah yes, my bad! (I actually even said it myself #16009 (comment) :-))

[TomAugspurger]

@jorisvandenbossche all good for you? Is everyone OK with a deprecation warning from pandas.formats.style, to be removed in 0.21?