Personal opinion. I think that Tav is a descendant of Charname from BG1-2. Of course that is pretty low hanging fruit, so I am probably wrong.
As far as it goes, I suspect that the artifact that Shadowhart has contains a bit of Bhaalspawn essence, and that is what is being collected. This works even if Tav isn't part of the lineage. That would be one way to tie things in with the original game, and would go a long way towards explaining why the group is being pursued/tested.
Anyway, speculation on no information.
VERY low hanging fruit, to the ground. Charname canonically gave up his/her Bhaalspawn essence to be mortal at the end of Throne of Bhaal. Even if Charname kept his/her portion of the essence like Abdel did, he/she would be targeted by Viekang too. Oh, and Bhaal is back from the dead. He's been back for a few years now, though nobody knows (except Wizards of the Coast and Larian Studios) what he has been up to since his return. And Shadowheart's artifact has Githyanki connections.
