IIRC, the GOG version of the game stores savegames in a subfolder of C:\GOG Games - but you've probably looked there? You can try opening a File Explorer in the root of C: and do a search for metadata.ion - a file which is found in every Thief 3 savegame folder.
If your saves are lost you can get back to the seaside mansion mission by starting over and skipping through the proper missions by pressing Shift+Ctrl+Alt+End at the start of each. (Note that End must be the last key pressed.) You have to play through the City segments, so use those to acquire enough loot to get you back on track. The T3 Gold mod must be enabled for the mission-ending function to work properly.
Another option is to continue from someone else's save.