[extractor/douyutv] fix broken DouyuTV and DouyuShow

[c-basalt]

IMPORTANT: PRs without the template will be CLOSED

Description of your pull request and other information

Use PhantomJS to enable the use of new APIs to fix DouyuTV (live stream) and DouyuShow (videos).

Fixes #2494
Fixes #7295

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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• I am the original author of this code and I am willing to release it under Unlicense
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What is the purpose of your pull request?

• Fix or improvement to an extractor (Make sure to add/update tests)
• New extractor (Piracy websites will not be accepted)
• Core bug fix/improvement
• New feature (It is strongly recommended to open an issue first)

Copilot Summary

🤖 Generated by Copilot at 0bd9507

Summary

🛠️📺🐛

Refactor and improve douyutv.py extractors. Create a new base class DouyuBaseIE and use it for DouyuTVIE and DouyuShowIE. Fix format and metadata extraction for Douyu livestreams and VODs.

DouyuBaseIE is the master of the stream
It spawns the subclasses with common genes
They rip the formats and metadata from the site
Refactoring the code with power and might

Walkthrough

• Introduce a new base class DouyuBaseIE for common logic of Douyu extractors (link)
• Update and fix the extraction of livestream formats and metadata in DouyuTVIE (link, link, link)
• Fix a typo in the DouyuTVIE class that used the wrong variable for room id (link)
• Add and update the extraction of VOD formats and metadata in DouyuShowIE (link, link)