feat: complete stage 4 cleanup and code formatting

This commit completes stage 4 of the refactoring plan, focusing on cleanup
and optimization of the modernized codebase.

## Key Changes

### Code Cleanup
- Remove legacy `src/lib/styles.ts` (no longer needed)
- Remove old modal components (`ImportProgressModal.tsx`, `ProviderList.tsx`)
- Streamline `src/lib/tauri-api.ts` from 712 lines to 17 lines (-97.6%)
  - Remove global `window.api` pollution
  - Keep only event listeners (`tauriEvents.onProviderSwitched`)
  - All API calls now use modular `@/lib/api/*` layer

### Type System
- Clean up `src/vite-env.d.ts` (remove 156 lines of outdated types)
- Remove obsolete global type declarations
- All TypeScript checks pass with zero errors

### Code Formatting
- Format all source files with Prettier (82 files)
- Fix formatting issues in 15 files:
  - App.tsx and core components
  - MCP management components
  - Settings module components
  - Provider management components
  - UI components

### Documentation Updates
- Update `REFACTORING_CHECKLIST.md` with stage 4 progress
- Mark completed tasks in `REFACTORING_MASTER_PLAN.md`

## Impact

**Code Reduction:**
- Total: -1,753 lines, +384 lines (net -1,369 lines)
- tauri-api.ts: 712 → 17 lines (-97.6%)
- Removed styles.ts: -82 lines
- Removed vite-env.d.ts declarations: -156 lines

**Quality Improvements:**
- ✅ Zero TypeScript errors
- ✅ Zero TODO/FIXME comments
- ✅ 100% Prettier compliant
- ✅ Zero `window.api` references
- ✅ Fully modular API layer

## Testing
- [x] TypeScript compilation passes
- [x] Code formatting validated
- [x] No linting errors

Stage 4 completion: 100%
Ready for stage 5 (testing and bug fixes)

src/App.tsx

@@ -11,7 +11,12 @@ import {
   useDeleteProviderMutation,
   useSwitchProviderMutation,
 } from "@/lib/query";
-import { providersApi, type AppType } from "@/lib/api";
+import {
+  providersApi,
+  settingsApi,
+  type AppType,
+  type ProviderSwitchEvent,
+} from "@/lib/api";
 import { extractErrorMessage } from "@/utils/errorUtils";
 import { AppSwitcher } from "@/components/AppSwitcher";
 import { ModeToggle } from "@/components/mode-toggle";
@@ -25,11 +30,6 @@ import UsageScriptModal from "@/components/UsageScriptModal";
 import McpPanel from "@/components/mcp/McpPanel";
 import { Button } from "@/components/ui/button";
 
-interface ProviderSwitchEvent {
-  appType: string;
-  providerId: string;
-}
-
 function App() {
   const { t } = useTranslation();
   const queryClient = useQueryClient();
@@ -56,7 +56,7 @@ function App() {
 
     const setupListener = async () => {
       try {
-        unsubscribe = await window.api.onProviderSwitched(
+        unsubscribe = await providersApi.onSwitched(
           async (event: ProviderSwitchEvent) => {
             if (event.appType === activeApp) {
               await refetch();
@@ -89,7 +89,7 @@ function App() {
   const handleOpenWebsite = useCallback(
     async (url: string) => {
       try {
-        await window.api.openExternal(url);
+        await settingsApi.openExternal(url);
       } catch (error) {
         const detail =
           extractErrorMessage(error) ||
@@ -127,13 +127,13 @@ function App() {
       if (activeApp !== "claude") return;
 
       try {
-        const settings = await window.api.getSettings();
+        const settings = await settingsApi.get();
         if (!settings?.enableClaudePluginIntegration) {
           return;
         }
 
         const isOfficial = provider.category === "official";
-        await window.api.applyClaudePluginConfig({ official: isOfficial });
+        await settingsApi.applyClaudePluginConfig({ official: isOfficial });
 
         toast.success(
           isOfficial
@@ -249,10 +249,7 @@ function App() {
 
           <div className="flex flex-wrap items-center gap-3">
             <AppSwitcher activeApp={activeApp} onSwitch={setActiveApp} />
-            <Button
-              variant="outline"
-              onClick={() => setIsMcpOpen(true)}
-            >
+            <Button variant="outline" onClick={() => setIsMcpOpen(true)}>
               MCP
             </Button>
             <Button onClick={() => setIsAddOpen(true)}>