DEPR: `DataFrame.to_latex` in favour of `Styler.to_latex`
The tracker of items needed to do before deprecating `DataFrame.to_latex()`.

- [x] acceptance of the `jinja2` requirement for LaTeX output, since `Styler` requires `jinja2`: this is blocker.
- [x] make Styler functional for all DataFrames (i.e. including non-unique columns, indexes) (#41269).
- [x] enhance for `longtable` keyword or other environments (#41866).
- [x] enhance for `caption` to allow short and long captions, and allow top/bottom caption placement. (#41659)
- [x] enhance with ability to style indexes/column headers with styles (e.g bold rows). (#41993)
- [x] enhance with an escape option for LaTeX characters. (#41619)
- [ ] <s>enhance `.hide_columns` with `.show_columns` alternative (optional)</s> not necessary
- [x] enhance `.hide_columns` and `.hide_index` to have dual function to hide the entire array, or specific items (#41266)
- [x] make styler reactive to separate sparse columns and index separately  (#41512)
- [x] acceptance of removal of specific kwargs and all formatting keyword args (see below).
- [ ] validation for ``column_format`` to pass tests or just rely on docs/duck typing?
- [x] validation for ``caption`` to pass tests (#43368) or just remove the validation in favour of duck typing?
- [x] ability to format index with a formatter #43101
- [x] separate `siunitx` for encapsulating headers in curly braces only when necessary #43397
- [x] index names removal #43346
- [x] Optionally use multirow / multicol or just blank out cells. #43369 #43382
- [x] fix bug: label doesnt render if a caption is not given (table and longtable) #43399

### Removed Keyword Args

`col_space`: **removed** since `Styler.to_latex()` does not necessarily produce display values of equal length, (this is a console display only arg)
`sparsify`: **replaced** by alternative kwargs `sparse_index` and `sparse_columns`
`multicolumn`, `multicolumn_format`, `multirow`: **replaced** by alternative kwargs `multirow_align` `multicol_align`
`formatters` `float_format` : **replaced** by the superior `df.style.format(...)` args
