If you're using zkLogin with Sui Wallet, you can indeed facilitate payments. Utilize the Enoki SDK for integrating zkLogin directly into your application. This SDK allows you to sign and execute transactions. To add a buy function, you'll need to create a transaction that transfers Sui, then sign and execute it.

Since you're using a direct connection setup, it is recommended to use the Enoki SDK. This will facilitate the integration effectively. Here's a link to the Enoki SDK documentation: Enoki SDK.