Migrating TimeMachine from Damaged HD to new HD

I second trying DiskWarrior. The internal HDD of my Fusion Drive iMac failed about a year ago and at that time my backup disk also got corrupted. DiskWarrior rebuilt the backup disk and restored it to a perfect working state while an Apple Authorized Service Provider put a new HDD into the iMac.

Manually coping over the Backups.backupdb folder may not work since Time Machine relies extensively on hard links, which allow for multiple exact copies of a file to link to the same written blocks on the drive. The hard links are likely not preserved during copying, and as a result the same files are written multiple times to different parts of the disk, instead of hard linking to a single place and saving storage space.

What you could try doing, though, is cloning your corrupted backup disk to a new drive via Disk Utility's restore function - this will preserve the hard links and save on storage space. However, it may carry over the corruption with it.

EDIT: Sorry, I replied to the wrong comment. Hopefully ASC staff will sort this out.

Time Machine: How to transfer backups from a current backup drive to a new backup drive

https://support.apple.com/en-us/HT202380

3-2-1 Backup Strategy: three copies of your data, two different methods, and one offsite.

Boot clone https://discussions.apple.com/docs/DOC-10081

How to use Time Machine to back up or restore your Mac: https://support.apple.com/en-us/HT201250

Use DiskUtility Restore feature https://support.apple.com/guide/disk-utility/restore-a-disk-dskutl14062/mac

I don't use Time Machine so I am unfamiliar with the details of the backup drive and whether it is possible to manually copy the whole backup. Maybe you can use Carbon Copy Cloner to transfer the backup.

Have you thought about using Disk Warrior to repair the HFS+ volume? There is no guarantee DW will fix it, but it has done a marvelous job for us over the years.