wip REF: redirect `df.to_html` to Styler if new kwargs are used.
This is an alternatative way of transitioning `DataFrame.to_html` to `Styler.to_html`.

It is a very minimalist introduction:

  - It will **fallback to the original HTMLFormatter implementation** if:
    - any of the deprecated kwargs are specifically input, and will show a **deprecation warning**.
    - **none** of the new Styler implementation kwargs are input.
  - It will **only use the new Styler implementation** if no deprecated kwargs are input and at least one **new** kwarg is used.


here is the rendered doc-strings:
<img width="602" alt="Screenshot 2022-01-02 at 15 46 11" src="https://user-images.githubusercontent.com/24256554/147883230-ff6e5e55-b30c-4429-bb9c-f6b4c6c0024c.png">
<img width="544" alt="Screenshot 2022-01-02 at 15 46 23" src="https://user-images.githubusercontent.com/24256554/147883233-d0b179a2-01ae-4a4a-b832-5666f13744dc.png">
<img width="571" alt="Screenshot 2022-01-02 at 15 46 34" src="https://user-images.githubusercontent.com/24256554/147883235-f37f1492-1526-47fe-aa73-db50f2a2e338.png">
<img width="561" alt="Screenshot 2022-01-02 at 15 46 45" src="https://user-images.githubusercontent.com/24256554/147883236-03132b3b-3626-4bb9-8948-07dc544b07a1.png">
<img width="574" alt="Screenshot 2022-01-02 at 15 46 56" src="https://user-images.githubusercontent.com/24256554/147883237-c589680e-4c8a-41e4-9c36-e8788701b364.png">
<img width="599" alt="Screenshot 2022-01-02 at 15 47 07" src="https://user-images.githubusercontent.com/24256554/147883238-c297586d-c5e4-4b19-87ea-4d1e64ccadb7.png">
<img width="606" alt="Screenshot 2022-01-02 at 15 47 17" src="https://user-images.githubusercontent.com/24256554/147883239-5e6607b9-dfc9-480a-97c2-3f35f2d855b4.png">
<img width="587" alt="Screenshot 2022-01-02 at 15 47 25" src="https://user-images.githubusercontent.com/24256554/147883240-658f752f-516d-4a80-963c-77a32289001d.png">
<img width="610" alt="Screenshot 2022-01-02 at 15 47 32" src="https://user-images.githubusercontent.com/24256554/147883242-6de1853c-04dc-4487-8173-41fd47c3f374.png">


This pull request is stale because it has been open for thirty days with no activity. Please [update](https://pandas.pydata.org/pandas-docs/stable/development/contributing.html#updating-your-pull-request) and respond to this comment if you're still interested in working on this. @attack68 do you still want to work on this? @datapythonista I do but it requires some pre requisites and a community consensus. There is a bit more progress on `DataFrame.to_latex`. Hopefully in future will try to use that as a template, so will close this for now.