I've alluded to something like this throughout multiple threads throughout the months, but my thoughts on this have been rather jumbled.
From playing the Wrath of the Righteous beta, there was a lot about the companions there that really leapt out to me. They bantered with each other frequently instead of largely only reacting to whatever the player character did, and had voice lines when a battle starts, while attacking, another line when landing a critical hit, and they even had voice lines whenever they succeeded a perception check to warn the rest of the party. There's also random banter between the party members when long resting too, though this point isn't very relevant in a comparison to BG3. There's even certain points in the game where you'll see certain companions talking to other NPCs on their own within the game's various hub areas as you progress. One moderately spoilery example of this:
One of the companions, the Zen Archer Lann, is a mongrelman who has spent the majority of his life living in underground caves. During chapter 2, when the fifth crusade begins and everyone is traveling on the road, you can find a crusader within the camp questioning Lann about why he keeps staring at the sky. He basically states that he's never really known what it's like to live with a wide open sky above him, and that he finds it fascinating and terrifying. The crusader assumes that the latter part means that he may be concerned about winged enemies attacking the camp and lightly mocks him for that concern, but it's a very valid threat to Lann because he never had to consider such a thing while living in the caves. Of course, the camp gets ambushed at night in that exact way later in the game, with Lann barging into your tent to make sure you haven't been ambushed while also complaining about how he had been warning the other archers to watch the sky. (The rest of the companions had already been taken or were fighting off the ambush in other parts of the camp, and slowly rejoin your party throughout that part of the game.)
After that part of the story is resolved, you can find Lann and the crusader talking to each other within the camp again, with the crusader vowing revenge against the demons for the events of the previous night. Both interactions are very easy to miss if you just head straight for the camp exit nearby.
The details are minor, but they add up over time to have a very subtle effect towards making the characters feel like they're a part of the world rather than relatively disconnected from it. Such things can be a very effective narrative tool - for example, some of the lines that one of the WotR companions says during combat basically clues the player in that they are not what they are presenting themselves as.
At the moment in regards to BG3, it feels like the only companions that really have any sort of non-neutral relationship with each other are Lae'zel and Shadowheart, although it may only be that way in my mind due to knowing certain spoiler information from datamines. The rest seem completely indifferent to each other, but may bicker from time to time about what they believe is useful at that very moment. There are hardly any moments where they will actually speak to each other on a personal level, but I recognize that it may also be a narrative limitation from how selfish/reserved they currently appear to be presented as. It's a big reason why there are complaints about the perceived asshole personalities/cynicism of the BG3 companions.
To shake off this image, you should consider livening up the companions with more smaller interactions and voice lines in general. Upon further thought, maybe you can try something that I don't recall ever seeing in any game period, and have voice lines for characters when attacking certain enemies. Bosses in games tend to have plenty of personal things to say to the player characters and companions, but I struggle to think of a game that actually takes advantage of the reverse too. For example, perhaps Wyll can have some choice lines when attacking goblins. Or Gale can try to be a smartass and display his supposedly superior intellect with snarky comments about less known creatures, like beholders at the start of an encounter against one (maybe even providing the player a clue as to what one of their weaknesses may be or what they are capable of). A water elemental could be Astarion's worst nightmare and should result in some really hilarious lines.
That said, since it's been several months since we've heard anything in regards to this game's development, it's possible a fair amount of the concerns I have here are already being addressed later on. But in the case it isn't, a thread is warranted.