Build the REST API with rate limiting and API keys

Create Next.js API routes for the CarbonLens public API:

1. POST /api/v1/calculate/transport.accepts transport parameters, returns emissions
2. POST /api/v1/calculate/energy.accepts energy usage (kWh, fuel type), returns emissions
3. POST /api/v1/calculate/diet.accepts meal description or diet type, returns daily/annual emissions
4. GET /api/v1/factors.returns all emission factors with sources

Requirements:

• API key authentication via x-api-key header
• Rate limiting: 100 requests/hour for free tier
• Consistent error response format: { error: string, code: string }
• OpenAPI/Swagger documentation comments
• Input validation with zod on all endpoints

Store API keys and usage counts in the database.