I personally enjoy how Pathfinder: Kingmaker/Wrath of the Righteous handles skill checks during their dialogue. While companions are part of your active party, their relevant skills are used for rolling skill checks if you pick an option where their skills are better than your own.
So when there is a history check option, when you hover your mouse over that specific item, the game's tooltip will tell you which character will be making that roll. If you have a companion with a higher skill in history than your own in your party, their skill will be used for the roll. If they are not in your active party, or your own skill is higher than anyone in your active party, your character's skills will be used in the roll.
I believe that system can still be used in Baldur's Gate 3 and work. If it's too much to add extra cutscenes where a companion will cut in and make certain rolls for you during dialogues, then the alternative can be to just simply have their skills be used instead of yours for the roll, and use the same cutscene as if your character would have done it with their own skill.
That way, it would feel like the party is actually working together. We don't need every single cutscene to be so reactive and to be different just because you used another character to make a roll for a dialogue choice for you.
Would it be nice to see Astarion cut in during a dialogue with a sleight of hand check and pickpocket the NPC in the cutscene? Yes, it would be pretty cool, but we wouldn't be losing much from having the normal cutscene of our character doing the pickpocketing using Astarion's skill. Would it look strange seeing your character not capable of pickpocketing pick a pocket? Yes, but I think that cosmetic issue is a far lesser issue of having a dialogue system that does not mix well with a party-based RPG.
There are also moments in Divinity Original Sin 2 where some companions would actually interrupt your dialogue with certain NPCs that were a part of their origin quest. You could allow them to talk to the NPC instead of your character to help advance their personal questline.
Edit:
Well, one of the very principles of a party-based RPG is,
precisely, to build a party with a reasonable range of skills, so that they can face a reasonable range of challenges. Part of the point (especially in a single-player, video game context) is in composing your party, then venturing forth in the world and seeing if the assembled roster works.
You won't pass every skill check. At best, you might have a tool for every situation (e.g. a companion with the appropriate Skill Proficiency), so you may have better odds. But success is not guaranteed.
Also, for me, it helps with roleplaying and immersion if I can have scenes that make sense.
- When walking in the swamp, if I have Lae'zel in front and the GM (i.e. the game) calls for an Ability Check (only one roll, from only one character, just because) to see if the group spots something, I'd like to choose my Druid or Gale for that roll. I don't like being told by the GM/game :
"Actually, you have roll with Lae'zel because she's in front. Yes, yes, I know, I would ask everyone to roll a Perception check to spot an ambush in the Blighted Village, because everyone cares about their skin, so it makes sense. And, yes, I would ask everyone to roll for Religion if you passed by a statue in a temple, because everyone has eyes and knowledge, and a tongue to share that knowlege, so it makes sense. But this is different. Completely different. Nothing in common. You are now in a cutscene. What is that, you ask ? Nevermind. But it means I can really have only one of you roll the dice. And you can't even choose who that character is. Well, you can, but for this you'd have to reload the game and use fore-knowledge. So just assume that everyone now doesn't care about their skin and trust the person in front to spot every danger."
- When walking into Kagha's first conversation with my PC, and hearing Wyll tell me "please, you have to do something for that child", I can't help thinking, "yeah, it would be great if I had someone in the party that I took with me mostly because he's good at Persuasion. Too bad I don't have someone like this in my party my PC isn't my party's Face".
I agree with everything said here, 100%. It highlights issues with the current dialogue system to a T, and I couldn't have said it better.