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/eslint.config.mjs

@@ -1,39 +1,3 @@
-// @ts-check
-import eslint from '@eslint/js';
-import eslintPluginPrettierRecommended from 'eslint-plugin-prettier/recommended';
-import globals from 'globals';
-import tseslint from 'typescript-eslint';
+import {node} from '@vigdorov/eslint-config';
 
-export default tseslint.config(
-  {
-    ignores: ['eslint.config.mjs', 'coverage'],
-  },
-  eslint.configs.recommended,
-  ...tseslint.configs.recommendedTypeChecked,
-  eslintPluginPrettierRecommended,
-  {
-    languageOptions: {
-      globals: {
-        ...globals.node,
-        ...globals.jest,
-      },
-      sourceType: 'commonjs',
-      parserOptions: {
-        projectService: true,
-        tsconfigRootDir: import.meta.dirname,
-      },
-    },
-  },
-  {
-    rules: {
-      '@typescript-eslint/no-explicit-any': 'off',
-      '@typescript-eslint/no-floating-promises': 'error',
-      '@typescript-eslint/no-unsafe-argument': 'error',
-      '@typescript-eslint/no-unsafe-assignment': 'error',
-      '@typescript-eslint/no-unsafe-call': 'error',
-      '@typescript-eslint/no-unsafe-member-access': 'error',
-      '@typescript-eslint/no-unsafe-return': 'error',
-      "prettier/prettier": ["error", { endOfLine: "auto" }],
-    },
-  },
-);
+export default node();