feat: creates backend for the project

backend/package.json

@@ -0,0 +1,30 @@
+{
+  "name": "@family-budget/backend",
+  "version": "0.1.0",
+  "private": true,
+  "scripts": {
+    "dev": "tsx watch src/app.ts",
+    "build": "tsc",
+    "start": "node dist/app.js",
+    "migrate": "tsx src/db/migrate.ts"
+  },
+  "dependencies": {
+    "@family-budget/shared": "*",
+    "cookie-parser": "^1.4.7",
+    "cors": "^2.8.6",
+    "dotenv": "^17.3.1",
+    "express": "^5.2.1",
+    "pg": "^8.19.0",
+    "uuid": "^13.0.0"
+  },
+  "devDependencies": {
+    "@types/cookie-parser": "^1.4.10",
+    "@types/cors": "^2.8.19",
+    "@types/express": "^5.0.6",
+    "@types/node": "^25.3.3",
+    "@types/pg": "^8.18.0",
+    "@types/uuid": "^10.0.0",
+    "tsx": "^4.21.0",
+    "typescript": "^5.9.3"
+  }
+}