Fix: Update youtubei.js Transcript Fetching Logic

[google-labs-jules]

The yt.getTranscript function call in background.js was causing a runtime error because it is no longer a valid function in youtubei.js v8.0.0. This fix replaces the deprecated function with the correct, multi-step API process for fetching transcripts. The new implementation first retrieves video information to find available caption tracks and then executes a get_transcript action to download the transcript data. This change successfully restores the extension's core functionality and improves error handling.

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PR created automatically by Jules for task 13865063330465325120

[google-labs-jules]

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