I agree that something's missing, and some of you here summed it up perfectly - in my eyes. The thing that would solve it would be Tav having their own arc developing in the game that the companions would react to same way we react to theirs.
That's what happened in BG1/BG2, we got to play a custom character (with a simple backstory, yes, but it was flexible enough to allow for all sorts of roleplaying around it). We played the Bhaalspawn and that alone - getting to discover things about my character, choosing how they react to it, and talking about it to NPCs was what made me attach to them and see them as a character in their own right. I don't agree hence that the Bhaalspawn was as bland as Tav is.
Things that come to mind quickly would be - if Tav, not Shadowheart, had the artifact, but didn't know where from and why (we could see her trying to steal it for added drama). We could have an arc about finding out what it is and how to make it protect our companions as well, making us both central to the story, useful to them, and having some interesting choices to make. Toss in some funky reveal about why we were the ones chosen to hold it and control it and there you have it.
Another thing that would help tremendously, I think, would be adding some more bits to say about our character while talking to companions. Ages ago, I played what was probably the best written romance mod for BG - Haer'Dalis romance for BG2. Not only was it unique and well done, but it was also smart about allowing the player to not only learn about the NPC, but to shape their PC increasing immersion and roleplay. AFAIR Haer, as a bard, wanted to write some sort of little chronicle about their perilous travels and would ask PC questions about their past, or their opinions about plot events. I remember it being *very* effective at creating the impression of conversations going both ways, developing the character, and forging a reasonable bond with the NPC
