feat: add JWT authentication

backend/package.json

@@ -13,7 +13,9 @@
   "license": "ISC",
   "type": "module",
   "devDependencies": {
+    "@types/bcryptjs": "^2.4.6",
     "@types/express": "^5.0.6",
+    "@types/jsonwebtoken": "^9.0.10",
     "@types/node": "^25.9.1",
     "@types/pg": "^8.20.0",
     "prisma": "^7.8.0",
@@ -24,9 +26,11 @@
   "dependencies": {
     "@prisma/adapter-pg": "^7.8.0",
     "@prisma/client": "^7.8.0",
+    "bcryptjs": "^3.0.3",
     "dotenv": "^17.4.2",
     "env-var": "^7.5.0",
     "express": "^5.2.1",
+    "jsonwebtoken": "^9.0.3",
     "pg": "^8.21.0"
   }
 }