[ie/generic] Improve direct video link ext detection

[bashonly]

Closes #8265

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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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 fe274d3

Summary

📁🔎📝

Improved file extension detection for generic extractor by using a helper function and passing the detected extension to the format info. This affects the file yt_dlp/extractor/generic.py.

urlhandle_detect_ext is the key to our salvation
We pass the ext to the format and unleash the extraction
No more generic errors, no more false detections
We improved the file extension detection

Walkthrough

• Import urlhandle_detect_ext function from utils.py to detect file extension from URL response (link)
• Modify determine_ext function to accept default_ext argument and return None if URL has no clear extension (link)
• Call urlhandle_detect_ext function with full_response object to get more accurate extension from response headers or content type (link)
• Add ext variable to f dictionary to pass extension information to downloader (link)