feat: add vitest for testing and implement tests for calculateDay utility

- Added "test" script to package.json for running vitest.
- Updated api.js to use localhost for backend during development.
- Created utils.spec.js to test calculateDay function with various scenarios.
- Updated vite.config.js to include vitest configuration and conditionally load Vue DevTools.

frontend/package.json

@@ -11,7 +11,8 @@
     "build": "vite build",
     "preview": "vite preview",
     "lint": "eslint . --fix",
-    "format": "prettier --write src/"
+    "format": "prettier --write src/",
+    "test": "vitest"
   },
   "dependencies": {
     "@jamescoyle/vue-icon": "^0.1.2",
@@ -30,8 +31,10 @@
     "eslint": "^9.31.0",
     "eslint-plugin-vue": "~10.3.0",
     "globals": "^16.3.0",
+    "jsdom": "^27.0.1",
     "prettier": "3.6.2",
     "vite": "^7.0.6",
-    "vite-plugin-vue-devtools": "^8.0.0"
+    "vite-plugin-vue-devtools": "^8.0.0",
+    "vitest": "^4.0.5"
   }
 }