refactor: remove deprecated tauri-api.ts file

- Delete src/lib/tauri-api.ts as event listener has been migrated
- Event listening now uses providersApi.onSwitched from lib/api/providers.ts
- All references to tauriEvents have been removed
- Type checking passes successfully

This completes the API layer cleanup from the refactoring plan (Phase 4).

src/lib/tauri-api.ts

@@ -1,17 +0,0 @@
-import { listen, type UnlistenFn } from "@tauri-apps/api/event";
-import type { AppType } from "@/lib/api";
-
-export interface ProviderSwitchedPayload {
-  appType: AppType;
-  providerId: string;
-}
-
-export const tauriEvents = {
-  onProviderSwitched: async (
-    handler: (payload: ProviderSwitchedPayload) => void,
-  ): Promise<UnlistenFn> => {
-    return await listen("provider-switched", (event) => {
-      handler(event.payload as ProviderSwitchedPayload);
-    });
-  },
-};