You're exactly right — if your Sui wallet is linked through a Google account (or another OAuth provider like Apple or Facebook), you cannot directly access the private key. These types of accounts use zero-knowledge login protocols, meaning there's no traditional passphrase or private key involved.

This presents a challenge when trying to interact with tools like the Sui CLI, which require direct access to a private key or keystore file.

Instead, your wallet is managed securely by the service (e.g., Sui Wallet app or Ethos), and all signing operations are done on your behalf behind the scenes.

If you need to work with the CLI or developer tools, the best approach is to:

• Create a new wallet using the Sui CLI that gives you full key access
• Transfer some funds to that address from your Google-linked wallet
• Use this CLI-managed wallet for development and scripting

Let me know if you'd like help generating a CLI wallet or moving funds over.

From what I understand, you can't directly get a private key from a Sui wallet linked through a Google account. These types of logins, using zero-knowledge proofs, don't involve a passphrase or private key, which poses a challenge when attempting to interact with the wallet through the command line interface.