REF: Transfer `DataFrame.to_latex` to `Styler` implementation for v1.5.0
State: closed

The latest version 1.4.0 issues a generic `FutureWarning` advising utilising `df.style.to_latex`, instead of `DataFrame.to_latex` suggesting arguments signature might change in future.

This PR makes the following changes for 1.5.0:

 - [x] creates a temporary function `DataFrame._to_latex_via_styler`. **This is the v.2.0 goal.**
 - [x] fully deprecates and no longer uses `col_space` which has no impact on LaTeX rendering and is not internally tested. Issues a direct `DeprecationWarning`.
 - [x] deprecates all other keyword arguments with a `FutureWarning` but refactors the internal call so that they still **pass all tests** (whitespace adjusted). (Note that `headers` as a list of `aliases` requires #45288 as pre-requisite, which is merged into this PR)
 - [x] implements the new keyword arguments allowing transference to the new signature. 

Indirect test impacts that are not just whitespace changes are **very minor**:

  - `test_to_latex_decimal` etc. inherits default precision from `pd.options.styler.format.precision`.
  -  `test_to_latex_empty_tabular` etc. renders a valid empty LaTeX table instead of invalid LaTeX.
  - `test_to_latex_longtable_with_index` drops curly braces on the _"continued on next page"_ comment.
  - `multirow` adds an alignment parameter which is available in newer LaTeX renderers.

# v1.5.0 Docstring:

![Screen Shot 2022-01-15 at 09 01 03](https://user-images.githubusercontent.com/24256554/149614526-b9b645a1-229d-4ec0-b4e3-1b5c6bc1cdee.png)
![Screen Shot 2022-01-15 at 09 01 19](https://user-images.githubusercontent.com/24256554/149614528-a3e731bb-bfee-4b76-9890-ce79e8f380fc.png)
![Screen Shot 2022-01-15 at 09 01 35](https://user-images.githubusercontent.com/24256554/149614535-fc0ed28b-949d-4f68-bce8-965eb588089f.png)
![Screen Shot 2022-01-15 at 09 01 48](https://user-images.githubusercontent.com/24256554/149614537-fdfbbcfa-da80-445c-84f0-37826352d7f2.png)

# v2.0 Goal Docstring:

![Screen Shot 2022-01-15 at 08 31 59](https://user-images.githubusercontent.com/24256554/149614364-e7bcd67e-7eae-4342-bf08-f9847614f4c5.png)





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name: Stale

Comments:
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.
Is this PR active? Could this be done in steps?
this pr is active, but depends on #45288 which I have tried to get a response to. There is push back to that which I need to either argue against persuasively or accept and close and then devise a new (more complicated way) to replicate the `header` arg here.

Can this be done in stages?
 - Currently it implements to 2.0 objective style `kwargs` pass through.
 - Deprecates all other non 2.0 kwargs and replicates their behaviour.

These are probably the only two separate PRs . The deprecations are all or nothing because if at least one deprecated arg is implemented with Styler then all need to be considered to get the final result right.
closed in favour of #47970