For iOS:
You can store your passkey in Apple’s “Passwords” app (available starting with iOS 18) or in other compatible apps such as Google Password Manager, Bitwarden, and similar services.
The passkey assistant will ask you which app you'd like to use to store your passkey.
For Android:
On Android devices, the passkey is stored by default in the Google Password Manager, provided it is enabled.
The passkey is stored encrypted on your device and can be synchronized via your Google account, for example, if you sign in on other devices with the same account.
If you use a different password manager such as Bitwarden or 1Password, and it supports passkeys, the passkey can also be stored there—as long as the manager is set as your default autofill service in the settings.