chore(13-01): install ESLint+Prettier, author flat config, wire lint/format scripts

- Install eslint@9.39.4 @eslint/js@9.39.4 typescript-eslint@8.61.0
  eslint-plugin-react@7.37.5 eslint-plugin-react-hooks@7.1.1
  eslint-config-prettier@10.1.8 prettier@3.8.4 as root devDependencies
- Author eslint.config.js: ignores → base recommendedTypeChecked (projectService:true)
  → pwa-react block (apps/pwa/** only) → disableTypeChecked override (config files +
  apps/api/tests) → prettier-last (eslint-config-prettier/flat)
- Add .prettierrc (singleQuote:true, printWidth:100) and .prettierignore
- Add "type":"module" to root package.json; add format/format:check scripts
- Add lint script (--max-warnings 0) to apps/api and apps/pwa

apps/api/package.json

@@ -9,6 +9,7 @@
     "start": "node dist/index.js",
     "test": "vitest run",
     "test:watch": "vitest",
+    "lint": "eslint src/ tests/ --max-warnings 0",
     "typecheck": "tsc --noEmit",
     "db:generate": "drizzle-kit generate",
     "db:migrate": "drizzle-kit migrate"