Add Codex auth preservation setting

src/i18n/locales/en.json

@@ -561,6 +561,9 @@
     "enableClaudePluginIntegrationDescription": "When enabled, the VS Code Claude Code extension provider will switch with this app",
     "skipClaudeOnboarding": "Skip Claude Code first-run confirmation",
     "skipClaudeOnboardingDescription": "When enabled, Claude Code will skip the first-run confirmation",
+    "codexAuth": "Codex Authentication",
+    "preserveCodexOfficialAuthOnSwitch": "Keep official login when switching third-party providers",
+    "preserveCodexOfficialAuthOnSwitchDescription": "When enabled, third-party Codex switches update only config.toml and keep the ChatGPT login in auth.json. When disabled, auth.json is overwritten with the active provider auth.",
     "appVisibility": {
       "title": "Homepage Display",
       "description": "Choose which apps to show on the homepage",

src/i18n/locales/ja.json

@@ -561,6 +561,9 @@
     "enableClaudePluginIntegrationDescription": "オンにすると VS Code の Claude Code 拡張のプロバイダーも同期します",
     "skipClaudeOnboarding": "Claude Code の初回確認をスキップ",
     "skipClaudeOnboardingDescription": "オンにすると Claude Code の初回インストール確認をスキップします",
+    "codexAuth": "Codex 認証",
+    "preserveCodexOfficialAuthOnSwitch": "サードパーティ切替時に公式ログインを保持",
+    "preserveCodexOfficialAuthOnSwitchDescription": "オンにするとサードパーティ Codex への切替では config.toml のみ更新し、auth.json の ChatGPT ログインを保持します。オフにすると auth.json を現在のプロバイダー認証で上書きします。",
     "appVisibility": {
       "title": "ホームページ表示",
       "description": "ホームページに表示するアプリを選択",

src/i18n/locales/zh-TW.json

@@ -561,6 +561,9 @@
     "enableClaudePluginIntegrationDescription": "開啟後 Vscode Claude Code 外掛程式的供應商將隨本軟體切換",
     "skipClaudeOnboarding": "跳過 Claude Code 初次安裝確認",
     "skipClaudeOnboardingDescription": "開啟後跳過 Claude Code 初次安裝確認",
+    "codexAuth": "Codex 認證",
+    "preserveCodexOfficialAuthOnSwitch": "切換第三方時保留官方登入",
+    "preserveCodexOfficialAuthOnSwitchDescription": "開啟後切換第三方 Codex 供應商只更新 config.toml，並保留 auth.json 中的 ChatGPT 登入狀態；關閉後會用目前供應商 auth 覆寫 auth.json。",
     "appVisibility": {
       "title": "主頁面顯示",
       "description": "選擇在主頁面顯示的應用程式",

src/i18n/locales/zh.json

@@ -561,6 +561,9 @@
     "enableClaudePluginIntegrationDescription": "开启后 Vscode Claude Code 插件的供应商将随本软件切换",
     "skipClaudeOnboarding": "跳过 Claude Code 初次安装确认",
     "skipClaudeOnboardingDescription": "开启后跳过 Claude Code 初次安装确认",
+    "codexAuth": "Codex 认证",
+    "preserveCodexOfficialAuthOnSwitch": "切换第三方时保留官方登录",
+    "preserveCodexOfficialAuthOnSwitchDescription": "开启后切换第三方 Codex 供应商只更新 config.toml，并保留 auth.json 中的 ChatGPT 登录态；关闭后会用当前供应商 auth 覆盖 auth.json。",
     "appVisibility": {
       "title": "主页面显示",
       "description": "选择在主页面显示的应用",