cgsecurity.org

Well, thank you very much for this comprehensive and extensive answer.
I guessed that I had dug my own grave when I re-formatted, but after the Freebox formatting the disk could not be read nor mounted, at least by the means within my reach (and I was a bit shocked).
Now to clarify a few points you ...

PhotoRec process screenshots (sorry, I see thet I can't really chose the order in which the attachments are displayed in my posts, but hopefully the file naming and the screenshots themselves are enough to understand what is what)

Following stages of TestDisk process: Partition choice menu, Quick Search stage, and results of said quick search. (next I'll post screenshots of PhotoRec use)

Thank you for your attention, and sorry for the abbreviations.
Here are the first 3 attachments: Log file, Mint's Disks window displaying the faulty ssd drive (unmounted), and TestDisk first partitions detection. (more to follow)

Greetings to all, and specially to the dev., for putting up these tools.
[edit] AND SORRY, I misclicked and posted the message too soon, completing it now.

First of all, I'll confess being the kind of "Jon Snow tech dude": knows nuthing, asks for help, get things done... often getting into trouble ...