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/client.gen.ts

@@ -0,0 +1,16 @@
+// This file is auto-generated by @hey-api/openapi-ts
+
+import { type ClientOptions, type Config, createClient, createConfig } from './client';
+import type { ClientOptions as ClientOptions2 } from './types.gen';
+
+/**
+ * The `createClientConfig()` function will be called on client initialization
+ * and the returned object will become the client's initial configuration.
+ *
+ * You may want to initialize your client this way instead of calling
+ * `setConfig()`. This is useful for example if you're using Next.js
+ * to ensure your client always has the correct values.
+ */
+export type CreateClientConfig<T extends ClientOptions = ClientOptions2> = (override?: Config<ClientOptions & T>) => Config<Required<ClientOptions> & T>;
+
+export const client = createClient(createConfig<ClientOptions2>());