refactor(providers): add flexible app type resolution with dual parameter support

Add `resolve_app_type` helper to support both enum and string-based app type
parameters across all provider commands. This change:

- Eliminates implicit default to Claude (previously used `unwrap_or`)
- Supports two parameter forms: `app_type` (enum, priority 1) and `app` (string, priority 2)
- Provides explicit error handling when both parameters are missing
- Updates all 14 provider command functions with consistent parameter validation
- Fixes tray menu provider switching to pass the new `app` parameter

This dual-parameter approach maintains backward compatibility while enabling
future CLI tool integration and more flexible API usage patterns.

Technical details:
- Priority order: `app_type` enum > `app` string > error
- Invalid `app` strings now return errors instead of defaulting
- All existing tests pass (45/45)

src/lib/api/providers.ts

@@ -15,31 +15,31 @@ export interface ProviderSwitchEvent {
 
 export const providersApi = {
   async getAll(appType: AppType): Promise<Record<string, Provider>> {
-    return await invoke("get_providers", { app_type: appType });
+    return await invoke("get_providers", { app: appType });
   },
 
   async getCurrent(appType: AppType): Promise<string> {
-    return await invoke("get_current_provider", { app_type: appType });
+    return await invoke("get_current_provider", { app: appType });
   },
 
   async add(provider: Provider, appType: AppType): Promise<boolean> {
-    return await invoke("add_provider", { provider, app_type: appType });
+    return await invoke("add_provider", { provider, app: appType });
   },
 
   async update(provider: Provider, appType: AppType): Promise<boolean> {
-    return await invoke("update_provider", { provider, app_type: appType });
+    return await invoke("update_provider", { provider, app: appType });
   },
 
   async delete(id: string, appType: AppType): Promise<boolean> {
-    return await invoke("delete_provider", { id, app_type: appType });
+    return await invoke("delete_provider", { id, app: appType });
   },
 
   async switch(id: string, appType: AppType): Promise<boolean> {
-    return await invoke("switch_provider", { id, app_type: appType });
+    return await invoke("switch_provider", { id, app: appType });
   },
 
   async importDefault(appType: AppType): Promise<boolean> {
-    return await invoke("import_default_config", { app_type: appType });
+    return await invoke("import_default_config", { app: appType });
   },
 
   async updateTrayMenu(): Promise<boolean> {
@@ -50,10 +50,7 @@ export const providersApi = {
     updates: ProviderSortUpdate[],
     appType: AppType,
   ): Promise<boolean> {
-    return await invoke("update_providers_sort_order", {
-      updates,
-      app_type: appType,
-    });
+    return await invoke("update_providers_sort_order", { updates, app: appType });
   },
 
   async onSwitched(