Here's what Karlach and Astarion get up to if you leave them at camp: Joining a D&D actual-play show
Roll for initiative.
I can't imagine why you'd leave both Karlach and Astarion out of your party, unless your version of Tav, the hero of Baldur's Gate 3, is some kind of obscene rogue/barbarian multiclass who has both their specialties covered. That's what happened at GenCon's live Dungeons & Dragons show, however, when voice actors Samantha Béart and Neil Newbon explored what their characters get up to when they wander off on their own, live on stage with Dungeon Master Aabria Iyengar and fellow players Anjali Bhimani (DesiQuest) and Brennan Lee Mulligan (Dimension 20).
Their adventure begins at a dive bar so low it's in the actual Underdark, but I won't spoil where it goes from there. Suffice to say it's an extremely silly good time, and the players get to take a couple of pot-shots at Gale and Lae'zel while they're not around. This is for sure the kind of shenanigans the NPCs get up to when I leave them behind, and that's canon.
The second half of the game includes a demonstration of Project Sigil, the 3D virtual tabletop Wizards of the Coast is currently working on. It looks a lot more graphically impressive than something like Roll20, which is what I'm using to run my current game of D&D, perhaps to a fault. There's a noticeable delay in the live game, and if your players don't have high-end desktop PCs I can see a virtual tabletop this graphically intense being a bit much.
The cast of Baldur's Gate 3, or at least its origin characters, previously played D&D on an episode of High Rollers (which gave us Bing Bong, an NPC so beloved Larian canonized them in the epilogue update), so they know their Constitution saves from their Charisma checks. A few years ago, Newbon even ran a campaign of Warhammer Fantasy Role-Play over Twitch if you needed another reason to love the man.