Add Amplitude backend

[vklimontovich]

Summary

Add Amplitude as a supported analytics backend.

Implementation

Use direct HTTP V2 API via fetch.

Why not use a library:

• @amplitude/analytics-node - uses native http module. Fails on Vercel Edge with "Can't resolve 'http'".
  Confirmed in Amplitude community.
• @amplitude/analytics-browser - client-side only, requires DOM

API endpoint: https://api2.amplitude.com/2/httpapi

Config

amplitudeBackend({
  apiKey: process.env.AMPLITUDE_API_KEY!,
  // optional: use EU data residency
  host?: "https://api.eu.amplitude.com"
})

Event mapping

• pageView -> Page Viewed event
• custom events -> pass through as-is
• anonymousUserId -> device_id
• userContext.userId -> user_id
• serverContext.ip -> ip
• client context -> platform, os_name, device_model, etc.