Does Portkey have a private key?

No. Your Portkey account is a virtual address controlled by manager addresses, not private keys. Manager addresses function as Externally Owned Accounts (EOAs) but are locally stored on the user's login device, eliminating the need for manual management.

Each manager address is device-specific and generated for devices where the user's account is logged in. As long as the account is logged in on a device, that device stores the corresponding manager address and private key information. Users won't interact with or directly utilise these manager addresses. They only need to operate the device, allowing the manager address to work behind the scenes and control the on-chain account, virtual address, for various tasks.