My experience says that the sword does grant regeneration but the regeneration is very SLOW. See the description of the sword. Therefore, it really is you AND the sword works.
Correct, it does not. Nevertheless, the sword regenerates HP. The simplest way to check it: give the sword to an injured character before travelling somewhere. As we know, we are not regenerating during a travel in BG2 but the character with the sword will do. Another possibility (for patient players): give the sword to a wounded character and wait at least 1 min of real time. The wounded character should get 1 - 2 HP.