Could you have logged in to a different user account? That would give a different set of profiles/saves, and trigger a prompt to create a new profile if you had not played from that account before.
Check the save folder to see if the saves and original profile are there, but not showing up in-game for some reason.
In Linux the saves are store in the Home directory, '..\Larian Studios\Divinity Original Sin Enhanced Edition\PlayerProfiles\<ProfileName>\Savegames_patch' folder.
You can try searching your hard drive for *.lsv files, in case the saves got moved somehow.
Do you have any recent backups of your home directory, where you may be able to recover any saves?
For the Steam version, if you had cloud saves enabled, you can check in the Steam install folder, as well, since Steam keeps a copy of the profile and saves there, which it uses when syncing online.
You may be able to check / download online saves for the Steam version with the program Steam Cloud File Manager Lite
); I'm not sure if it can be run in Linux. You need to be logged in to the Steam client and have the game's AppID (373420).
Alternately, you can log into Steam in a browser and use this link
(this will also let you download saves, if available, but you would need to manually rename them, as Steam combines the path and name together for the online name).