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

package.json

@@ -1,6 +1,7 @@
 {
   "name": "familysync",
   "private": true,
+  "type": "module",
   "packageManager": "pnpm@11.5.1",
   "scripts": {
     "dev:api": "pnpm --filter @familysync/api dev",
@@ -9,6 +10,17 @@
     "test": "pnpm --filter @familysync/api test",
     "test:e2e": "pnpm --filter @familysync/pwa test:e2e",
     "lint": "pnpm -r --if-present lint",
-    "typecheck": "pnpm -r typecheck"
+    "typecheck": "pnpm -r typecheck",
+    "format": "prettier --write .",
+    "format:check": "prettier --check ."
+  },
+  "devDependencies": {
+    "@eslint/js": "9.39.4",
+    "eslint": "9.39.4",
+    "eslint-config-prettier": "10.1.8",
+    "eslint-plugin-react": "7.37.5",
+    "eslint-plugin-react-hooks": "7.1.1",
+    "prettier": "3.8.4",
+    "typescript-eslint": "8.61.0"
   }
 }