How to restore a stolen or seriously damaged USB drive previously saved with time machine ?

By the way can you confirm that the content of each "aged" folder (e.g. 2023-05-31-121530 for may 31, 12:15:30) is the full back-up of that date and not an incremental back-up, i.e. the changes since previous back-up ?

No, each one contains the new files with pointers yo the last new files which has the newest changed files with pointers to the last changed files, a infinitum.

Reboot the Mac into Recovery mode with the external Time Machine drive connected. Run Disk Utility First Aid on that main TM drive name. When you see a green completion, reboot the Mac normally removing the external drive before the Mac actually reboots.

In System Preferences > Time Machine, switch it off as you don't want the current operating system to write to it. Mount the older Time Machine drive, and then launch the /Applications/Time Machine.app to present your Restore interface with past dates on it. You use this mode for the purpose of restoring a file or folder, but not as a full Time Machine restore.

How to mitigate the damage? Just don't do it. Don't attempt to access a TM dataset with Finder.

I can't confirm anything on any drive you have. How would you even think that possible in a forum comment?

Once you enter the Time Machine, you restore files and folders. What era they come from is your choice.

Théo de France wrote:

No, no and no, ku4hx

The best answer to mitigate a risk is to specify which action will lead to a damage in order to avoid to do it. It is not to do nothing at all.

The question is not about confirming something about a specific drive…. That I have no more because it has been stolen. The question is about recovering its back-up from an healthy TM drive and an healthy Mac, so it is possible to explain that in a forum.

And again the issue is that when entering in TM , TM don’t allow you to restore a file / a folder previously saved in TM from a drive not currently connected to a Mac… or, if it allows it, the way of doing it is well hidden.

Whit that it seems useless that you continue to comment this thread this way.

I am not certain what you're asking, and interpreting a lot-of-words question can be a challenge for me.

Time Machine can restore what it backs up, using the Time Machine interface.

It's not all that good at restoring external devices.

The following seems to maybe be discussing the same thing that you're asking about, but I'm guessing:

https://apple.stackexchange.com/questions/366466/how-to-restore-external-hard-drive-from-time-machine-backup-the-right-way

Attach it to a Mac that has TM capability. Opening a TM dataset with a Finder type app can, and often does, damage the data.