Imagine Dark Urge being a companion. Like you meet them over some corpses of fishermen, and they just look confused, but not actually disturbed by all the blood and guts. They have amnesia, don't remember how they got on the ship, who they were before. So while every companion carefully tells you who they are or what they did, D!Urge just hums at your question with a faraway gaze.
Then one night, you wake up to someone cackling and find your bedroll with drops of blood, and D!Urge just standing there, with a dagger and bloodied hands over someone's mangled body. So you have to pass perception and make a choice to attack them, wake everyone up, or just go back to sleep.
And they just throw unsettling comments and jokes about corpses and their lost memories. Like "Have I been there before?" and "That one would've looked pretty as a corpse"
Once you learn about the Dead Three and their Chosen, D!Urge will have a cutscene where they'll tell you of their suspicion, after they read accounts about the Bhaalspawn.
If you romance them, they'll wake you up in the Act II with a dagger in their hand, telling you they will kill you if you don't do something about it. So you'll need to pass checks on strength, perception, or you will get slaughtered. And they'll have to revive you.
People in Moonrise towers keep being mean to you if you have D!Urge in your party, and then you learn they were here before, they just don't remember it.
And you'll have one more reason to flatten Gortash into a pancake. And Orin. And you can either help D!Urge become the Chosen, or reject their father, and like with Astarion they may leave your party, or make you their unholy assassin, so you will have to take an oath, knowing they'll kill you one day, or if they reject Bhaal, they'll ask you if you still want them, because they still don't remember a thing and they have no idea how to be with someone.
After the endgame battle, you can clear the Bhaal murderers together, help them with finding families of those they killed, or find a cure for their amnesia, or, if they are the Chosen, keep on killing everyone, but then you won't be in an Epilogue, and it will say D!Urge killed you in the middle of the day, and that's how they got in jail.
I just think of watching D!Urge from the side, through the eyes of another character will be so strange and weird, and their story crosses the main plot so much, like they are practically one of the three baddies. The accusations of them being behind all of them having tadpoles, like if you as leader don't have a good relationship with your companions, some of them may even leave after learning you let D!Urge stay. So many possibilities.