Upgrade of computer and use of Backup Disk

Makusuto posed this question, but I would like to reframe it.

I had a MacBook Pro (mid-2012, Retina display). I backed it up using Time Machine on a G-Drive (8TB capacity). There is available space on it.

I upgraded my computer because I needed to run Big Sur, so I purchased a MacBook Pro (late 2020, M1), and decommissioned the old MacBook Pro (requiem in pace, old friend). Now, I want to use the G-Drive for my Time Machine backups. In plugging the drive in, and opening Time Machine, I am provided the option to … "Claim Existing Backups", "Start new Backup", "Decide Later", because the old backups on the drive were created by my old MacBook Pro.

Apple does not provide info as to what specifically occurs if one were to choose any of the three options. If the first, will my new machine be able to access the old backups (as the older machine is completely erased and returned to Apple, no other machine could access them)? If the second, would the new machine backups erase the old, and start anew)? If the third, what happens if I were to start using the drive to back up my new machine?

Thanks.