I'll start by saying that my issue is incredibly similar to Mac stuck in restart cycle after failed macOS Catalina update but being a new user I couldn't comment there nor I had any answers unfortunately.
A relative brought me is Mac stuck in the reboot loop, he doesn't have recent backups to restore from and can't lose the files stored on the disk (yeah..... I know....) . Trying to reinstall Mojave on the same disk via recovery mode causes the exact same loop with same error message (not enough free space).
Ideally I would have booted the Mac from another drive, cleaned up / backed up some files to make more free space and proceeded with normal installation BUT, once I mount the HD of the troubled Mac, I see 2 partitions :
1)"Backup (Original Drive Name)" - 480 GB large but no files visible
2) "Macintosh HD" - appears to contain only Mac installation files
Basically I can't find the original files, I'm guessing that during the installation process OSX installer created a backup partition (1) and would have restored the files once installation was complete, but don't know how to access those files.
Anybody knows of at least a way to access the files in what appears to be a backup partition created by the installer ?
Sorry for the almost duplicate question and great thanks to all for reading.