One thing that is sticking at me is that while all the companions have these deep backstories, the custom character, "Tav," has none. You make a Githyanki and they don't know any Githyanki lore and Lae'zel has to explain it all to them. You play as a cleric of Shar and Shadowheart has to teach them all about Shar. If you were at the table and there was something that you didn't already pick up from researching your character, you would at least get a knowledge check with a high bonus because this is basic stuff that you need to know if you are that thing. Being a druid certainly lets you have knowledge of Sylvanus - but being a Gith or Cleric of Shar leaves you clueless.
So, rather than just the simplified DnD 5e backgrounds, you really should add backstories for different races and classes that you can select separately. They don't need to be detailed and fleshed out like the companions, but if I am a Githyanki, let me pick whether I'm some orphan raised by elves and don't know a thing about being Gith or if I'm well versed or betrayed my queen. Very basic things that can direct how much my character knows and a few dialogue options other than being "Baldurian." Must my elf be from Baldur's gate? If so, is she going to know anyone when she gets there or do we just assume she has neighbors and friends she just doesn't interact with throughout the game? We need something basic here when surrounded by these fleshed out companions.