I'm not sure what accidental journey through Gmail's options OP took but it looks to me that they inadvertently started setting up a passkey, which is tied to the hardware but can sync between Apple devices using iCloud Keychain. Apple certainly isn't blocking you from changing Gmail-specific settings.
In this situation, I suspect it's being forced because 2-factor authentication is on, so the user has to continue on a device that has been previously been trusted.