Yes, progress is transferred as long as you are playing both the main game and the demo on the same platform and using the same account on your platform (i.e. the same Steam/Xbox Live/PSN account).
Please note that the Epic Games Store and Steam are considered two separate platforms. Therefore progress from the Steam demo will not transfer to the Epic Games Store version of the full game, and vice versa.
Please note that the Epic Games Store and Steam are considered two separate platforms. Therefore progress from the Steam demo will not transfer to the Epic Games Store version of the full game, and vice versa.