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/AppSwitcher.tsx

@@ -1,13 +1,13 @@
-import type { AppType } from "@/lib/api";
+import type { AppId } from "@/lib/api";
 import { ClaudeIcon, CodexIcon } from "./BrandIcons";
 
 interface AppSwitcherProps {
-  activeApp: AppType;
-  onSwitch: (app: AppType) => void;
+  activeApp: AppId;
+  onSwitch: (app: AppId) => void;
 }
 
 export function AppSwitcher({ activeApp, onSwitch }: AppSwitcherProps) {
-  const handleSwitch = (app: AppType) => {
+  const handleSwitch = (app: AppId) => {
     if (app === activeApp) return;
     onSwitch(app);
   };