iMac Catalina version 10.15.7
iMac Catalina version 10.15.7 and Time Machine both 8 years old. Time Machine stuck in Verify Backup mode. When I replace the Mac will the Time Machine automatically finish the Verify Backup process?
Is this what you're asking about? https://support.apple.com/guide/mac-help/if-your-new-mac-inherits-your-backup-history-mh35732/mac
Or are you asking will TM simply pick up on the new Mac where it left off on the old Mac?
I think it's simpler, and more straight forward, to dedicate a new external HDD to the new Mac, and keep the old backup as a standby until you know you no longer need it.
Of course, there's the question of usability of the current backup in data migration if it never finishes a task.