You can store your passkey in the “Passwords” app (available from iOS 18) or in Apple’s iCloud Keychain.
When setting up your passkey, the passkey assistant will ask which app you’d like to use for storing it.
To check or manage this setting, follow these steps:
From iOS 18:
Settings → General → Autofill & Passwords
From iOS 16.4:
Settings → Apple ID section (at the top, with your name) → iCloud → Keychain
Enable iCloud Keychain if it’s not already activated.