Your Id-Extras license is linked to your Adobe Creative Cloud account, not to a specific computer.
So if you make sure to log in to the same Adobe account on the new computer as you were using on the old, damaged computer, there should be no problem activating the script on the new computer.
See also here: https://www.id-extras.com/reactivation-woes-youve-got-new-computer-doesnt-let-activate-product
Does that help?
I am using Adobe InDesign version CC 2019-v14.0.2-x64-PORTABLE. So the Id-Extras license is not linked to my Adobe Creative Cloud account.
So is there a way to backup the Id-Extras license and reuse it when my computer crashes or switch to InDesign CC 2020 – v15?
Looking forward to receiving a reply from you.