BUG: `Styler.to_latex` now doesn't manipulate the `Styler` object.
- [x] closes #42320 
- [x] tests added / passed
- [x] whatsnew entry not needed if included in 1.3.0 (although will be needed for 1.3.1)

> [ ] whatsnew entry (probably for 1.3.1)

you can put in 1.3.0 for review purposes and move later. (after #42312)

although there seems to be conda-incubator/setup-miniconda@v2 issues today which could slow down the ability to release > > [ ] whatsnew entry (probably for 1.3.1)
> 
> you can put in 1.3.0 for review purposes and move later. (after #42312)
> 
> although there seems to be conda-incubator/setup-miniconda@v2 issues today which could slow down the ability to release

if thats the case then not technically necessary for 1.3.0 (it fixes a feature that was added for 1.3.0) @jreback ok for 1.3 (we have issues with #42304 that's blocking release) @meeseeksdev backport 1.3.x thanks @attack68  Something went wrong ... Please have  a look at my logs. @attack68 

shouldn't the following render the output as Latex in a notebook?

```
df = pd.DataFrame([[1, 2.2, "dogs"], [3, 4.4, "cats"], [2, 6.6, "cows"]],
                  index=["ix1", "ix2", "ix3"],
                  columns=["Integers", "Floats", "Strings"])
s = df.style.highlight_max(
    props='cellcolor:[HTML]{FFFF00}; color:{red};'
          'textit:--rwrap; textbf:--rwrap;'
)

from IPython.display import display, Latex
display(Latex(s.to_latex()))
``` @jreback I don't use LaTeX much in a notebook but I believe Jupyter uses MathJax to render and Mathjax does not support all LaTeX environements including tabular, so this just displays as text in a box. 