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>

backend/tsconfig.json

@@ -1,25 +1,16 @@
 {
+  "extends": "@vigdorov/typescript-config/node",
   "compilerOptions": {
     "module": "nodenext",
     "moduleResolution": "nodenext",
     "resolvePackageJsonExports": true,
-    "esModuleInterop": true,
-    "isolatedModules": true,
-    "declaration": true,
-    "removeComments": true,
-    "emitDecoratorMetadata": true,
-    "experimentalDecorators": true,
-    "allowSyntheticDefaultImports": true,
     "target": "ES2023",
-    "sourceMap": true,
     "outDir": "./dist",
     "baseUrl": "./",
-    "incremental": true,
-    "skipLibCheck": true,
     "strictNullChecks": true,
-    "forceConsistentCasingInFileNames": true,
     "noImplicitAny": false,
     "strictBindCallApply": false,
+    "strictPropertyInitialization": false,
     "noFallthroughCasesInSwitch": false
   }
 }