Add auto-generated API client and update authStore tests

- Integrated OpenAPI-generated TypeScript SDK (`sdk.gen.ts`, `types.gen.ts`, `client.gen.ts`) for API interactions.
- Refactored `authStore` tests to include storage mock reset logic with default implementations.

frontend/src/lib/api/generated/index.ts

@@ -1,8 +1,4 @@
-// This file will be auto-generated by running: npm run generate:api
-// Make sure the backend is running before generating the API client
-//
-// To generate: npm run generate:api
-//
-// This placeholder prevents import errors before generation
+// This file is auto-generated by @hey-api/openapi-ts
 
-export {}
+export type * from './types.gen';
+export * from './sdk.gen';