[extractor/niconico] Download comments from the new endpoint

[Lesmiscore]

Closes #6760

IMPORTANT: PRs without the template will be CLOSED

Description of your pull request and other information

ADD DESCRIPTION HERE

Fixes #6760

Things to consider:

• new and legacy formats have different structure; should we assign an another language for the new one?

Template

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• At least skimmed through contributing guidelines including yt-dlp coding conventions
• Searched the bugtracker for similar pull requests
• Checked the code with flake8 and ran relevant tests

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• Fix or improvement to an extractor (Make sure to add/update tests)
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• Core bug fix/improvement
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