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/tsconfig.json

@@ -0,0 +1,13 @@
+{
+  "extends": "@mosaic/config/typescript/nestjs",
+  "compilerOptions": {
+    "outDir": "./dist",
+    "rootDir": "./src",
+    "baseUrl": "./",
+    "paths": {
+      "@/*": ["src/*"]
+    }
+  },
+  "include": ["src/**/*"],
+  "exclude": ["node_modules", "dist", "**/*.spec.ts", "**/*.test.ts"]
+}