Google Authenticator after an iphone motherboard replacement

A little while back my iPhone X started having motherboard issues and was unable to be booted up. I was using Google Authenticator to store many accounts, some of which may be impossible to get to without those codes. From what I understand **Google Authenticator is tied to your hardware**, and as a result when I restored my icloud backup to a new phone, the Google Authenticator keys are lost. This leaves me no choice but to try to get the old iPhone working so I can safely restore an iCloud backup to it and have the google authenticator codes appear again. If it’s the same phone this will work fine. The question is: If the phones motherboard is replaced, does that effectively change the hardware so much that google authenticator won’t recognize it as being the same phone?