refactor(api): simplify app type parameter handling to single required parameter

Replace the previous dual-parameter approach (app_type/app/appType) with a single required `app: String` parameter across all Tauri commands. This change:

- Introduces unified `parse_app()` helper replacing complex `resolve_app_type()` logic
- Updates all backend commands in config, mcp, and provider modules
- Aligns frontend API calls to use consistent `app` parameter naming
- Simplifies MSW test handlers by removing optional parameter handling

This improves API clarity and reduces parameter ambiguity while maintaining backward compatibility through error handling.

src/lib/api/settings.ts

@@ -31,11 +31,11 @@ export const settingsApi = {
   },
 
   async getConfigDir(appType: AppType): Promise<string> {
-    return await invoke("get_config_dir", { app_type: appType });
+    return await invoke("get_config_dir", { app: appType });
   },
 
   async openConfigFolder(appType: AppType): Promise<void> {
-    await invoke("open_config_folder", { app_type: appType });
+    await invoke("open_config_folder", { app: appType });
   },
 
   async selectConfigDirectory(defaultPath?: string): Promise<string | null> {

src/lib/api/usage.ts

@@ -6,7 +6,7 @@ export const usageApi = {
   async query(providerId: string, appType: AppType): Promise<UsageResult> {
     return await invoke("query_provider_usage", {
       provider_id: providerId,
-      app_type: appType,
+      app: appType,
     });
   },
 };

src/lib/api/vscode.ts

@@ -11,7 +11,7 @@ export interface EndpointLatencyResult {
 
 export const vscodeApi = {
   async getLiveProviderSettings(appType: AppType) {
-    return await invoke("read_live_provider_settings", { app_type: appType });
+    return await invoke("read_live_provider_settings", { app: appType });
   },
 
   async testApiEndpoints(
@@ -29,7 +29,7 @@ export const vscodeApi = {
     providerId: string,
   ): Promise<CustomEndpoint[]> {
     return await invoke("get_custom_endpoints", {
-      app_type: appType,
+      app: appType,
       provider_id: providerId,
     });
   },
@@ -40,7 +40,7 @@ export const vscodeApi = {
     url: string,
   ): Promise<void> {
     await invoke("add_custom_endpoint", {
-      app_type: appType,
+      app: appType,
       provider_id: providerId,
       url,
     });
@@ -52,7 +52,7 @@ export const vscodeApi = {
     url: string,
   ): Promise<void> {
     await invoke("remove_custom_endpoint", {
-      app_type: appType,
+      app: appType,
       provider_id: providerId,
       url,
     });
@@ -64,7 +64,7 @@ export const vscodeApi = {
     url: string,
   ): Promise<void> {
     await invoke("update_endpoint_last_used", {
-      app_type: appType,
+      app: appType,
       provider_id: providerId,
       url,
     });