Shadowheart is the companion with the biggest mystery, which imo adds a lot to her interestingness as a companion.
-Astarion we immediately know is a vampire. He tells us his life story fairly easily.
-Lae'zel also just tells us her story/goals. The biggest mysteries involving her is the Gith artefact and if there actually is a purification process, which tbf aren't her mysteries. Oh, and I suppose it's unclear whether she might be an actual gith princess or she might just have an overinflated sense of importance, but the game doesn't really emphasize this (I'm mostly certain it's the latter).
-Gale might or might not be telling the truth about his history, but there's no mystery to solve. Just a task to complete.
-Wyll's lover is the biggest mystery involving him, but even that is a kind of straightforward task. Find girl. Rescue girl.

SH requires a lot of work to learn her story, and even then there is this mysterious artefact and her unknown past.