DOC: Rewrite for `Styler` user guide with new features and other high-level changes.
- [x] closes #39593
- [x] closes #40645 
- [x] Ensure all linting tests pass, see [here](https://pandas.pydata.org/pandas-docs/dev/development/contributing.html#code-standards) for how to run them
- [ ] whatsnew entry

This renames `Styling` with `Table Visualization` and aligns it more with `Chart Visualization`.

It re-organises some of the `Styler` user guide, removing outdated material, including new material with examples.
Hello @attack68! Thanks for updating this PR. We checked the lines you've touched for [PEP 8](https://www.python.org/dev/peps/pep-0008) issues, and found:



There are currently no PEP 8 issues detected in this Pull Request. Cheers! :beers: 

##### Comment last updated at 2021-03-18 07:01:26 UTC I think I have fixed up all my changes. So this **should be good to review**

The check failure on building docs I think is unrelated, although I'm not sure since I don't have much experience with this. If someone can confirm I would be pleased to learn. 

It seems to fail due to **1 warning** which I think is this:

```
reading sources... [ 96%] user_guide/enhancingperf
In file included from /home/runner/miniconda3/envs/pandas-dev/lib/python3.8/site-packages/numpy/core/include/numpy/ndarraytypes.h:1822,
                 from /home/runner/miniconda3/envs/pandas-dev/lib/python3.8/site-packages/numpy/core/include/numpy/ndarrayobject.h:12,
                 from /home/runner/miniconda3/envs/pandas-dev/lib/python3.8/site-packages/numpy/core/include/numpy/arrayobject.h:4,
                 from /home/runner/.cache/ipython/cython/_cython_magic_c8551c86669c6133a0e9bb5b383abbbf.c:630:
/home/runner/miniconda3/envs/pandas-dev/lib/python3.8/site-packages/numpy/core/include/numpy/npy_1_7_deprecated_api.h:17:2: warning: #warning "Using deprecated NumPy API, disable it with " "#define NPY_NO_DEPRECATED_API NPY_1_7_API_VERSION" [-Wcpp]
   17 | #warning "Using deprecated NumPy API, disable it with " \
      |  ^~~~~~~
In file included from /home/runner/miniconda3/envs/pandas-dev/lib/python3.8/site-packages/numpy/core/include/numpy/ndarraytypes.h:1822,
                 from /home/runner/miniconda3/envs/pandas-dev/lib/python3.8/site-packages/numpy/core/include/numpy/ndarrayobject.h:12,
                 from /home/runner/miniconda3/envs/pandas-dev/lib/python3.8/site-packages/numpy/core/include/numpy/arrayobject.h:4,
                 from /home/runner/.cache/ipython/cython/_cython_magic_1f3f4faa63381d31bc6688d149dcf218.c:631:
/home/runner/miniconda3/envs/pandas-dev/lib/python3.8/site-packages/numpy/core/include/numpy/npy_1_7_deprecated_api.h:17:2: warning: #warning "Using deprecated NumPy API, disable it with " "#define NPY_NO_DEPRECATED_API NPY_1_7_API_VERSION" [-Wcpp]
   17 | #warning "Using deprecated NumPy API, disable it with " \
      |  ^~~~~~~
```

```
build finished with problems, 1 warning.
Error: Process completed with exit code 1.
``` deleted



 sorry this got a bit lost can you merge master and update anything if needed @jreback there might be a few things to add soon, so ill wait and ping. Then you only have to review/download once 
[rendered_html.zip](https://github.com/pandas-dev/pandas/files/6174368/rendered_html.zip)

After splitting the PR  and updating this for most recent PRs here is the current rendered user guide.
 can you show a rendered view > can you show a rendered view

I've zipped the HTML above, (just the one page - user guide). I couldn't publish an image here since the page is too long.  @jreback this addresses only PRs that have been merged. I won't add anything further to it (except suggested changes),

For any other PRs that go into 1.3 I will submit a smaller change to the user guide afterwards just addressing those. Latest render: 
[Archive.zip](https://github.com/pandas-dev/pandas/files/6217273/Archive.zip)
 > Thanks! This looks really great. Requests below are mostly grammar nit-picks, some more opinionated than others. Push back if you disagree on any.

thanks @rhshadrach for going over it in such detail! I noticed a few of these myself previously but needed a prod to actually implement the fixes! hmm some ci / checks are failing. > hmm some ci / checks are failing.

@jreback these seem unrelated. I will merge and push > > hmm some ci / checks are failing.
> 
> @jreback these seem unrelated. I will merge and push

right yeah this was the first one i looked :-<, yep they are unrealted ok. ping on greenish. @jreback this is green-ish, green-er than before now anyway. thanks @attack68 pls check the built docs after they are built > thanks @attack68 pls check the built docs after they are built

will do.