[Nate] Add new site

[Hyeeji]

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• Searched the bugtracker for similar pull requests
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• Read youtube-dl coding conventions and adjusted the code to meet them
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• Bug fix
• Improvement
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• New feature

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Description of your pull request and other information

Closes #30236, qv.

[gerori]

已经收到您的来信，谢谢

[dirkf]

Or at least, it's not unicode. In yt-dl str should almost always be compat_str, but as above it's not needed here.

[dirkf]

I've adapted the yt-dlp code that derived from this PR and updated this PR accordingly, with additional error-handling. The download tests all passed locally.

Testers welcome.