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>

packages/shared/package.json

@@ -0,0 +1,40 @@
+{
+  "name": "@mosaic/shared",
+  "version": "0.0.1",
+  "private": true,
+  "main": "./dist/index.js",
+  "types": "./dist/index.d.ts",
+  "exports": {
+    ".": {
+      "types": "./dist/index.d.ts",
+      "require": "./dist/index.js",
+      "import": "./dist/index.js"
+    },
+    "./types": {
+      "types": "./dist/types/index.d.ts",
+      "require": "./dist/types/index.js",
+      "import": "./dist/types/index.js"
+    },
+    "./utils": {
+      "types": "./dist/utils/index.d.ts",
+      "require": "./dist/utils/index.js",
+      "import": "./dist/utils/index.js"
+    }
+  },
+  "scripts": {
+    "build": "tsc",
+    "dev": "tsc --watch",
+    "lint": "eslint src/",
+    "lint:fix": "eslint src/ --fix",
+    "typecheck": "tsc --noEmit",
+    "clean": "rm -rf dist",
+    "test": "vitest run",
+    "test:watch": "vitest",
+    "test:coverage": "vitest run --coverage"
+  },
+  "devDependencies": {
+    "@mosaic/config": "workspace:*",
+    "typescript": "^5.8.2",
+    "vitest": "^3.0.8"
+  }
+}