Remove Official YouTube API Fallback

[google-labs-jules]

The user requested to remove the official YouTube Data API method for fetching transcripts. This change deletes the fetchTranscriptWithOfficialApi function and updates the handleCopyTranscript and handleSummarizeInStudio functions to only use the primary youtubei.js library method.

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PR created automatically by Jules for task 3979377358170617411

[google-labs-jules]

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