Upgrade ESLint from 8 to 9 with flat config migration

Replace .eslintrc.cjs with eslint.config.mjs, upgrade eslint-plugin-vue
to 10, eslint-plugin-cypress to 6, @vue/eslint-config-prettier to 10,
and remove @rushstack/eslint-patch.

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

eslint.config.mjs

@@ -0,0 +1,17 @@
+import js from "@eslint/js";
+import pluginVue from "eslint-plugin-vue";
+import pluginCypress from "eslint-plugin-cypress";
+import skipFormatting from "@vue/eslint-config-prettier";
+
+export default [
+  {
+    files: ["**/*.{js,mjs,cjs,ts,vue}"],
+    ...js.configs.recommended,
+  },
+  ...pluginVue.configs["flat/essential"],
+  skipFormatting,
+  {
+    files: ["cypress/e2e/**/*.{cy,spec}.{js,ts,jsx,tsx}"],
+    ...pluginCypress.configs.recommended,
+  },
+];