Verify fullstack scaffold builds

- Install bun dependencies and generate bun.lock
- Add @types/bun to API dev dependencies for Bun type support
- Add @types/react and @types/react-dom to web dev dependencies
- Fix web tsconfig.node.json composite project emit configuration
- Verify all packages typecheck and build successfully
- Verify API health and status endpoints respond correctly

All verification steps passed:
- bun install: 354 packages installed
- packages/shared typecheck: OK
- packages/shared build: OK (dist generated)
- apps/api typecheck: OK
- apps/api build: OK (0.76 MB bundle)
- apps/web typecheck: OK
- apps/web build: OK (dist generated)
- API /health endpoint: {"status":"ok"}
- API /api/v1/status endpoint: {"name":"ZeaVis Edu","status":"ok","version":"0.1.0"}

apps/api/package.json

@@ -17,6 +17,7 @@
     "postgres": "^3.4.5"
   },
   "devDependencies": {
+    "@types/bun": "latest",
     "drizzle-kit": "^0.27.1",
     "typescript": "^5.6.3"
   }

apps/web/package.json

@@ -24,6 +24,8 @@
     "zustand": "^5.0.1"
   },
   "devDependencies": {
+    "@types/react": "^18.3.3",
+    "@types/react-dom": "^18.3.0",
     "autoprefixer": "^10.4.20",
     "postcss": "^8.4.49",
     "tailwindcss": "^3.4.15",

apps/web/tsconfig.node.json

@@ -2,7 +2,7 @@
   "extends": "../../tsconfig.base.json",
   "compilerOptions": {
     "composite": true,
-    "noEmit": true,
+    "noEmit": false,
     "module": "ESNext",
     "moduleResolution": "Bundler",
     "types": ["node"]