When the Safari extension is unlocked, it does not lock itself upon restarting the device. Additionally, if it is locked (and the device is restarted), it allows biometrics to be used to unlock it even when the app hasn’t been unlocked at least once (the app disallows biometrics to be used on the initial unlock after a restart of the device, which the extension should mirror).
1Password Version: 7.9.3
Extension Version: Not Provided
OS Version: iOS 15.2