refactor(web): migrate to TypeScript + standard Vue3 structure

memora-web/package.json

@@ -5,6 +5,7 @@
   "type": "module",
   "scripts": {
     "dev": "vite",
+    "typecheck": "vue-tsc --noEmit",
     "build": "vite build",
     "preview": "vite preview"
   },
@@ -15,7 +16,11 @@
     "vue-router": "^4.3.0"
   },
   "devDependencies": {
+    "@types/node": "^25.3.1",
     "@vitejs/plugin-vue": "^5.0.4",
-    "vite": "^5.1.6"
+    "sass": "^1.97.3",
+    "typescript": "^5.9.3",
+    "vite": "^5.1.6",
+    "vue-tsc": "^3.2.5"
   }
 }