(backend): Implement Flashcard Generation with Gemini AI

[07CalC]

Context

The core feature! Generate flashcards from topic content using AI. The generate.ts router has skeleton endpoints that need implementation.

Goal

• Fetch user's API key from settings
• Call Gemini API with topic content
• Parse response into flashcards
• Save flashcards to database
• Return generated flashcards to client

Files to Modify

• packages/api/src/routers/generate.ts
• Create packages/api/src/utils/gemini.ts

Deliverables

• Gemini API utility function
• Flashcard generation endpoint works end-to-end
• Proper error handling (no API key, API errors, parse errors)
• Flashcards saved to database
• Returns generated flashcards to client

[ishanrajsingh]

claim

[07CalC]

@ishanrajsingh you can't have more than one issue in the same repo

[Aryan0512398]

Claim

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/info

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[07CalC]

@Aryan0512398 yours