Update docs to new frontend/UI
We can have the docstrings of the properties that are missing docstrings (from discussion [here](https://github.com/huggingface/doc-builder/pull/96)) here by using your new `inject_arrow_table_documentation` onthem as well ? @sgugger & @lhoestq could you help me with what should the `docs` section in setup.py be changed to [here](https://github.com/huggingface/datasets/blob/master/setup.py#L212-L227) ?

as a reference, here is a transformers setup.py docs [section](https://github.com/huggingface/transformers/blob/master/setup.py#L304-L308) For now, you can put an empty list. Once the `doc-builder` is in a PyPi package (with the bug we fixed on Datasets but still waiting on the standing PR with the code switch) we can put it there. None of those dependencies are needed from this list?

```py
    "docs": [
        "docutils==0.16.0",
        "recommonmark",
        "sphinx==3.1.2",
        "sphinx-markdown-tables",
        "sphinx-rtd-theme==0.4.3",
        "sphinxext-opengraph==0.4.1",
        "sphinx-copybutton",
        "fsspec<2021.9.0",
        "s3fs",
        "sphinx-panels",
        "sphinx-inline-tabs",
        "myst-parser",
        "Markdown!=3.3.5",
    ],
``` No, that was all for sphinx. The only thing needed to build the doc is a pip install of `doc-builder` (only from git right now). @lhoestq feel free to request reviews from other maintainers 😊 Thanks ! @mariosasko and @albertvillanova feel free to take a look :)
I can do a thorough review this afternoon
### TLDR: Update `datasets` `docs` to the new syntax (markdown and mdx files) & frontend (as how it looks on [hf.co/transformers](https://huggingface.co/docs/transformers/index))

| Light mode                                                                                 | Dark mode                                                             |
|-----------------------------------------------------------------------------------------------------|--------------------------------------------------------------------------------|
| <img width="400" alt="Screenshot 2022-02-17 at 14 15 34" src="https://user-images.githubusercontent.com/11827707/154489358-e2fb3708-8d72-4fb6-93f0-51d4880321c0.png">    | <img width="400" alt="Screenshot 2022-02-17 at 14 16 27" src="https://user-images.githubusercontent.com/11827707/154489596-c5a1311b-181c-4341-adb3-d60a7d3abe85.png">                                     |

## Checklist

- [x] update datasets docs to new syntax (should call `doc-builder convert`) (this PR)
- [x] discuss `@property` methods frontend https://github.com/huggingface/doc-builder/pull/87
- [x] discuss `inject_arrow_table_documentation` (this PR) https://github.com/huggingface/datasets/pull/3690#discussion_r801847860
- [x] update datasets docs path on moon-landing https://github.com/huggingface/moon-landing/pull/2089
- [x] convert pyarrow docstring from Numpydoc style to groups style  https://github.com/huggingface/doc-builder/pull/89(https://stackoverflow.com/a/24385103/6558628)
- [x] handle `Raises` section on frontend and doc-builder https://github.com/huggingface/doc-builder/pull/86
- [x] check imgs path (this PR) (nothing to update here)
- [x] doc exaples block has to follow format `Examples::` https://github.com/huggingface/datasets/pull/3693
- [x] fix [this docstring](https://github.com/huggingface/datasets/blob/6ed6ac9448311930557810383d2cfd4fe6aae269/src/datasets/arrow_dataset.py#L3339) (causing svelte compilation error)
- [x] Delete sphinx related files 
- [x] Delete sphinx CI
- [x]  Update docs config in setup.py
- [x] add `versions.yml` in doc-build  https://github.com/huggingface/doc-build/pull/1
- [x] add `versions.yml` in doc-build-dev https://github.com/huggingface/doc-build-dev/pull/1
- [x] https://github.com/huggingface/moon-landing/pull/2089
- [ ] create new github actions. (can probably be in a separate PR) (see the transformers equivalents below)
1. [build_dev_documentation.yml](https://github.com/huggingface/transformers/blob/ad7390636d78346384ab79d45a65b8a9d59116c0/.github/workflows/build_dev_documentation.yml)
2. [build_doc_test.yml](https://github.com/huggingface/transformers/blob/7e61d56a45c19284cfda0cee8995fb552f6b1f4e/.github/workflows/build_doc_test.yml)
3. [build_documentation.yml](https://github.com/huggingface/transformers/blob/6950ccec1b7d59d32d0311619b1de8f20f219b8d/.github/workflows/build_documentation.yml)
4. [delete_dev_documentation.yml](https://github.com/huggingface/transformers/blob/ad7390636d78346384ab79d45a65b8a9d59116c0/.github/workflows/delete_dev_documentation.yml)
5. [doctests.yml](https://github.com/huggingface/transformers/blob/9f831bdeaf965acca6c6097dfffb1364f4416c17/.github/workflows/doctests.yml)

## Note to reviewers

The number of changed files is a lot (100+) because I've converted all `.rst` files to `.mdx` files & they are compiling fine on the svelte side (also, moved all the imgs to to [doc-imgs repo](https://huggingface.co/datasets/huggingface/documentation-images/tree/main/datasets)). Moreover, you should just review them on preprod and see if the rendering look fine.
_Therefore, I'd suggest to focus on the changed_ **`.py`** and **CI files** (github workflows, etc. you can use [this filter here](https://github.com/huggingface/datasets/pull/3690/files?file-filters%5B%5D=.py&file-filters%5B%5D=.yml&show-deleted-files=true&show-viewed-files=true)) during the review & ignore `.mdx` files. (if there's a bug in `.mdx` files, we can always handle it in a separate PR afterwards).