chore(client): add lint, format and test tooling

Configure ESLint 10 (flat, Vue + a11y), Prettier, Vitest + @vue/test-utils + jsdom, and add npm scripts for lint/format/test. Document VITE_API_BASE_URL.

client/eslint.config.js

@@ -0,0 +1,29 @@
+import js from '@eslint/js'
+import prettier from 'eslint-config-prettier'
+import pluginVue from 'eslint-plugin-vue'
+import vueA11y from 'eslint-plugin-vuejs-accessibility'
+import globals from 'globals'
+import tseslint from 'typescript-eslint'
+
+export default tseslint.config(
+  { ignores: ['dist/**', 'node_modules/**', 'coverage/**'] },
+  js.configs.recommended,
+  ...tseslint.configs.recommended,
+  ...pluginVue.configs['flat/recommended'],
+  ...vueA11y.configs['flat/recommended'],
+  {
+    files: ['**/*.{ts,vue}'],
+    languageOptions: {
+      globals: { ...globals.browser },
+      parserOptions: {
+        parser: tseslint.parser,
+        ecmaVersion: 'latest',
+        sourceType: 'module',
+      },
+    },
+    rules: {
+      'vue/multi-word-component-names': 'off',
+    },
+  },
+  prettier,
+)