Welcome to the forum @Camille
You can look (maybe with ls -lrt) in .config/Duplicati in root’s home directory for recent databases.
If you find a Duplicati-server.sqlite, that’s its job configurations. Random-letter.sqlite are the job databases.
Assuming distro and folder layout stay the same, databases that still match destination can just be moved.
EDIT:
Migration to new PC - faq wanted is on Windows but gives the same steps with a little bit more information.
I’m not quite sure what you have on the rebuilt computer now.