chore: migrate to @vigdorov/* shared configs (eslint, prettier, typescript, vite)

Replace project-local ESLint, Prettier, TypeScript, and Vite configs
with shared packages from dev-configs monorepo.

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

package.json

@@ -23,7 +23,9 @@
     "db:down": "docker-compose down"
   },
   "devDependencies": {
-    "concurrently": "^9.1.2"
+    "@vigdorov/prettier-config": "^1.0.0",
+    "concurrently": "^9.1.2",
+    "prettier": "^3.5.3"
   },
   "dependencies": {
     "class-transformer": "^0.5.1",