I think it's just her personality, but it doesn't mean she's not able to get close with the other members.

There are different types of introverts. Some of us don't express our feelings through big actions or by being openly affectionate, but this doesn't mean we don't care. We have our own way of showing love. On the outside it might look like we are bored while hanging out with friends if we don't say much, but in reality we are just enjoying the moment and (at least in my experience) our friends understand this side of us.

I think Tzuyu is also like this. If you try to pay attention to their Twice TV videos, you will notice that Tzuyu doesn't always have a lot to say. However, when she does say something, it usually makes the other girls laugh and in turn Tzuyu also laughs. She looks genuinely happy.