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

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

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

package.json

@@ -37,6 +37,9 @@
     "@eslint/eslintrc": "^3.2.0",
     "@eslint/js": "^9.18.0",
     "@nestjs/cli": "^11.0.0",
+    "@vigdorov/eslint-config": "^1.0.1",
+    "@vigdorov/prettier-config": "^1.0.0",
+    "@vigdorov/typescript-config": "^1.1.0",
     "@nestjs/schematics": "^11.0.0",
     "@nestjs/testing": "^11.0.1",
     "@swc/cli": "^0.6.0",