feat: add standalone YouTube transcript downloads

[lmdevv]

Summary

Adds standalone transcript downloads for YouTube videos.

• Adds a captions download mode to the API and web app.
• Supports plain text, WebVTT, SRT, and Markdown output.
• Selects manual captions first, with automatic captions as a fallback.
• Supports preferred caption language selection.
• Adds a separate plain-text transcript URL for copying.
• Adds transcript settings, API documentation, and unit tests.

Motivation

Cobalt already supports attaching subtitles to downloaded media through #1370. This adds the related use case of downloading the transcript without downloading the video or audio.

Scope

• YouTube is currently supported.
• The feature uses captions provided by YouTube. It does not generate transcripts with speech-to-text.
• WebVTT output preserves the source cues.
• Converted formats normalize caption markup and do not preserve stylized subtitle rendering.

Testing

• pnpm run --prefix api test:unit
• Existing API and web CI checks

Related issues

• Related to #368
• Related to #1001
• Related to #1196