feat: add support for YouTube Kids (#291)

* dev: add `WEB_KIDS` innertube client

* refactor: move DASH manifest stuff out of `VideoInfo`
This makes it easier to use these functions elsewhere.

* feat(ytkids): add `Kids#getInfo()` & `Kids#search()`

* feat: add `Innertube#kids.getHomeFeed()`

* docs: add YouTube Kids API ref

* docs: fix typo

* docs: fix yet another typo

* docs: update YouTube Music API ref
Unrelated but required to reflect changes made to the DASH manifest generation functions

* chore: lint

* chore: add tests

* feat: include `captions` in `VideoInfo`

* chore: fix tests

docs/API/kids.md

@@ -0,0 +1,85 @@
+# YouTube Kids
+
+YouTube Kids is a modified version of the YouTube app, with a simplified interface and curated content. This class allows you to interact with its API.
+
+## API
+  
+* Kids
+  * [.search(query)](#search)
+  * [.getInfo(video_id)](#getinfo)
+  * [.getHomeFeed()](#gethomefeed)
+
+<a name="search"></a>
+### search(query)
+
+Searches the given query on YouTube Kids.
+
+**Returns:** `Promise.<Search>`
+
+| Param | Type | Description |
+| --- | --- | --- |
+| query | `string` | The query to search |
+
+
+<details>
+<summary>Methods & Getters</summary>
+<p>
+
+- `<search>#page`
+  - Returns the original InnerTube response(s), parsed and sanitized.
+
+</p>
+</details> 
+
+<a name="getinfo"></a>
+### getInfo(video_id)
+
+Retrieves video info.
+
+**Returns:** `Promise.<VideoInfo>`
+
+| Param | Type | Description |
+| --- | --- | --- |
+| video_id | `string` | The video id |
+
+<details>
+<summary>Methods & Getters</summary>
+<p>
+
+- `<info>#toDash(url_transformer?)`
+  - Generates a DASH manifest from the streaming data.
+
+- `<info>#chooseFormat(options)`
+  - Selects the format that best matches the given options. This method is used internally by `#download`.
+
+- `<info>#download(options?)`
+  - Downloads the video.
+
+- `<info>#addToWatchHistory()`
+  - Adds the video to the watch history.
+
+- `<info>#page`
+  - Returns the original InnerTube response(s), parsed and sanitized.
+
+</p>
+</details> 
+
+<a name="gethomefeed"></a>
+### getHomeFeed()
+
+Retrieves the home feed.
+
+**Returns:** `Promise.<HomeFeed>`
+
+<details>
+<summary>Methods & Getters</summary>
+<p>
+
+- `<feed>#selectCategoryTab(tab: string | KidsCategoryTab)`
+  - Selects the given category tab.
+
+- `<feed>#categories`
+  - Returns available categories.
+
+- `<feed>#page`
+  - Returns the original InnerTube response(s), parsed and sanitized.