Repository: yt-dlp
Issue: [Twitch] VOD rechat isn't complete (saves only first X messages, missing pagination)
Labels: site-enhancement

### Checklist

- [X] I'm reporting a broken site
- [X] I've verified that I'm running yt-dlp version **2022.04.08** ([update instructions](https://github.com/yt-dlp/yt-dlp#update)) or later (specify commit)
- [X] I've checked that all provided URLs are alive and playable in a browser
- [X] I've checked that all URLs and arguments with special characters are [properly quoted or escaped](https://github.com/ytdl-org/youtube-dl#video-url-contains-an-ampersand-and-im-getting-some-strange-output-1-2839-or-v-is-not-recognized-as-an-internal-or-external-command)
- [X] I've searched the [bugtracker](https://github.com/yt-dlp/yt-dlp/issues?q=) for similar issues including closed ones. DO NOT post duplicates
- [X] I've read the [guidelines for opening an issue](https://github.com/yt-dlp/yt-dlp/blob/master/CONTRIBUTING.md#opening-an-issue)
- [X] I've read about [sharing account credentials](https://github.com/yt-dlp/yt-dlp/blob/master/CONTRIBUTING.md#are-you-willing-to-share-account-details-if-needed) and I'm willing to share it if required

### Region

_No response_

### Description

The Twitch VOD chat recording isn't complete, since yt-dlp lacks an ability to properly paginate VOD comments.
When it calls API for this:
https://github.com/yt-dlp/yt-dlp/blob/10fa2471fc11d6b63773b663ef0c431b0ce2bde4/yt_dlp/extractor/twitch.py#L418
It doesn't use `_next` field, provided in JSON response to get next comments and so on.
To fix this, you'd need to call this method again, providing page token as `cursor` parameter: `https://api.twitch.tv/v5/videos/<VOD ID>/comments?cursor=<value from _next field>`, while `_next` field exists.

For example from verbose log, `_next` field looks something like this:
```json
"_next":"eyJpZCI6Ij...VueEFBIn0f"
```

### Verbose log

```shell
[debug] Command-line config: ['-vU', '--no-download', '--write-subs', 'https://twitch.tv/videos/1475813279']
[debug] Encodings: locale cp1252, fs utf-8, out utf-8, err utf-8, pref cp1252
[debug] yt-dlp version 2022.04.08 [7884ade] (win_exe)
[debug] Python version 3.8.10 (CPython 64bit) - Windows-10-10.0.22000-SP0
[debug] Checking exe version: ffmpeg -bsfs
[debug] Checking exe version: ffprobe -bsfs
[debug] exe versions: ffmpeg 2021-12-30-git-12f21849e5-full_build-www.gyan.dev (setts), ffprobe 2021-12-30-git-12f21849e5-full_build-www.gyan.dev
[debug] Optional libraries: brotli, certifi, Cryptodome, mutagen, sqlite, websockets
[debug] Proxy map: {}
Latest version: 2022.04.08, Current version: 2022.04.08
yt-dlp is up to date (2022.04.08)
[debug] [twitch:vod] Extracting URL: https://twitch.tv/videos/1475813279
[twitch:vod] 1475813279: Downloading stream metadata GraphQL
[twitch:vod] 1475813279: Downloading video access token GraphQL
[twitch:vod] 1475813279: Downloading m3u8 information
[debug] Formats sorted by: hasvid, ie_pref, lang, quality, res, fps, hdr:12(7), vcodec:vp9.2(10), acodec, filesize, fs_approx, tbr, vbr, abr, asr, proto, vext, aext, hasaud, source, id
[debug] Downloading subtitles: rechat
[debug] Default format spec: bestvideo*+bestaudio/best
[info] v1475813279: Downloading 1 format(s): 1080p60
[info] Writing video subtitles to: OceanBlock Mod Pack! [1.16.5 _ Day 5] _ !patreon !prime !discord [v1475813279].rechat.json
[debug] Invoking downloader on "https://api.twitch.tv/v5/videos/1475813279/comments?client_id=kimne78kx3ncx6brgo4mv6wki5h1ko"
[debug] File locking is not supported on this platform. Proceeding without locking
[download] Destination: OceanBlock Mod Pack! [1.16.5 _ Day 5] _ !patreon !prime !discord [v1475813279].rechat.json
[download] 100% of 53.78KiB in 00:00
```