What I would like is if the group members also pair up with each other and not necessarily only with the player character.

It doesn't have to and shouldn't always be about a real couple bond, but also about deep friendships without any sex stuff. Especially between two men or two women.
This would also have an effect on the gameplay if you have the couple or the two friends with you and they save each other in battle, or if one of them falls, gets angry and lunges out of control at the killer, etc.

So also in the game then behave differently than the rest of the group. Does not have to be completely exaggerated, of course, but you should find it here and there, even in conversation options when playing.

In addition, I would always find it good if such a group then after a certain time together and many passed situations also noticeably grows into a unit and it then feels as if you are like a loving family. So the conversations and comments become softer, you apologize sometimes if you have said a stupid word, but not dramatically, but normal around flow.

I had this feeling a little bit in Dragon Age Origins at the very beginning of the Wood Elf campaign, when Merrill says something stupid in the group, but apologizes gently in the conversation and the situation felt and sounded very familiar and cohesive.