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