feat(context): add NestJS backend, PostgreSQL database, and migrate web app from Supabase to API

- Create NestJS backend on port 3020 with 4 modules (space, document, ai, token)
- Add Drizzle schema with 5 tables (spaces, documents, token_transactions, model_prices, user_tokens)
- Rewrite web services (spaces, documents, tokens, ai) to use shared API client instead of Supabase
- Move AI API keys server-side (Azure OpenAI, Google Gemini)
- Add seed script for model prices (gpt-4.1, gemini-pro, gemini-flash)
- Add 70 unit tests across 4 test suites (space, document, token, ai services)
- Add monorepo integration (setup-databases.sh, generate-env.mjs, docker init-db, root scripts)
- Remove @supabase/supabase-js dependency and delete supabase.ts from web app
- Update CLAUDE.md with full API documentation

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

apps/context/package.json

@@ -3,6 +3,9 @@
 	"version": "1.0.0",
 	"private": true,
 	"scripts": {
-		"dev": "pnpm --filter @context/mobile dev"
+		"dev": "turbo run dev",
+		"dev:web": "pnpm --filter @context/web dev",
+		"dev:backend": "pnpm --filter @context/backend dev",
+		"dev:mobile": "pnpm --filter @context/mobile dev"
 	}
 }