My kid is shy about her speech around others. Shyness is normal but I would think in nursery, somewhere he is weekly/daily, he would say some basics at least. Is he new at nursery? Maybe overtime he’ll open up. Shyness isn’t concerning but babbling is a little concerning truthfully but maybe he’s mimicking his little sister since that’s the only person he’s comfortable with there. If he’s speaking well at home then I wouldn’t be too concerned but I’d probably go along with the speech therapy anyway. It’s a good resource.
I think it is totally normal for a child to act differently in a different environment! And especially to feel more vulnerable than at home! But then in the flip of that, certain behaviours might not show with you because he is safe and you are his routine!