feat(#1): Set up monorepo scaffold with pnpm workspaces + TurboRepo

Implements the foundational project structure including:
- pnpm workspaces configuration
- TurboRepo for build orchestration
- NestJS 11.1.12 API (apps/api)
- Next.js 16.1.6 web app (apps/web)
- Shared packages (config, shared, ui)
- TypeScript strict mode configuration
- ESLint + Prettier setup
- Vitest for unit testing (19 passing tests)

Fixes #1

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

apps/api/package.json

@@ -0,0 +1,40 @@
+{
+  "name": "@mosaic/api",
+  "version": "0.0.1",
+  "private": true,
+  "scripts": {
+    "build": "nest build",
+    "dev": "nest start --watch",
+    "start": "node dist/main",
+    "start:debug": "nest start --debug --watch",
+    "start:prod": "node dist/main",
+    "lint": "eslint \"src/**/*.ts\"",
+    "lint:fix": "eslint \"src/**/*.ts\" --fix",
+    "typecheck": "tsc --noEmit",
+    "clean": "rm -rf dist",
+    "test": "vitest run",
+    "test:watch": "vitest",
+    "test:coverage": "vitest run --coverage",
+    "test:e2e": "vitest run --config ./vitest.e2e.config.ts"
+  },
+  "dependencies": {
+    "@nestjs/common": "^11.1.12",
+    "@nestjs/core": "^11.1.12",
+    "@nestjs/platform-express": "^11.1.12",
+    "@mosaic/shared": "workspace:*",
+    "reflect-metadata": "^0.2.2",
+    "rxjs": "^7.8.1"
+  },
+  "devDependencies": {
+    "@mosaic/config": "workspace:*",
+    "@nestjs/cli": "^11.0.6",
+    "@nestjs/schematics": "^11.0.1",
+    "@nestjs/testing": "^11.1.12",
+    "@swc/core": "^1.10.18",
+    "@types/express": "^5.0.1",
+    "@types/node": "^22.13.4",
+    "typescript": "^5.8.2",
+    "unplugin-swc": "^1.5.2",
+    "vitest": "^3.0.8"
+  }
+}