refactor(types): rename AppType to AppId for semantic clarity

Rename `AppType` to `AppId` across the entire frontend codebase to better
reflect its purpose as an application identifier rather than a type category.
This aligns frontend naming with backend command parameter conventions.

Changes:
- Rename type `AppType` to `AppId` in src/lib/api/types.ts
- Remove `AppType` export from src/lib/api/index.ts
- Update all component props from `appType` to `appId` (43 files)
- Update all variable names from `appType` to `appId`
- Synchronize documentation (CHANGELOG, refactoring plans)
- Update test files and MSW mocks

BREAKING CHANGE: `AppType` type is no longer exported. Use `AppId` instead.
All component props have been renamed from `appType` to `appId`.

src/components/settings/DirectorySettings.tsx

@@ -3,7 +3,7 @@ import { FolderSearch, Undo2 } from "lucide-react";
 import { Input } from "@/components/ui/input";
 import { Button } from "@/components/ui/button";
 import { useTranslation } from "react-i18next";
-import type { AppType } from "@/lib/api";
+import type { AppId } from "@/lib/api";
 import type { ResolvedDirectories } from "@/hooks/useSettings";
 
 interface DirectorySettingsProps {
@@ -14,9 +14,9 @@ interface DirectorySettingsProps {
   onResetAppConfig: () => Promise<void>;
   claudeDir?: string;
   codexDir?: string;
-  onDirectoryChange: (app: AppType, value?: string) => void;
-  onBrowseDirectory: (app: AppType) => Promise<void>;
-  onResetDirectory: (app: AppType) => Promise<void>;
+  onDirectoryChange: (app: AppId, value?: string) => void;
+  onBrowseDirectory: (app: AppId) => Promise<void>;
+  onResetDirectory: (app: AppId) => Promise<void>;
 }
 
 export function DirectorySettings({