Are Smaller Unis More Nuturing? Your experiences please

I don’t think you should pursue this investigatory route, OP. Instead you need to guide him towards choosing a handful of universities that seem to offer exactly the course he wants to study. Then visit, virtually or in person, so he can see where he might feel at home (as regards town and university environment). Refine list, fill out UCAS form ...

I was a very shy, socially awkward 18yr old. I found that starting in a totally alien environment allowed me to reset and forced me to communicate. Most people who know me now would not recognise the 18yr old me.
I suspect that leaving home and the protective, easy environment kick started the latent party animal.
My DS 16 is acutely aware of his social awkwardness and has been frustrated over the last 18mnths that he has lost touch with his social group. However he has managed to find a girlfriend and realised that he has been overthinking the awkwardness. He has started to go to parties and reintegrating. Teenage angst affects every single one of them, it’s just that some are just better at faking it.
The best Uni will be the one that does the best course. He will thank you in the future if you guide his choice based on his current social needs.
Most 15/16yr old boys are socially awkward, don’t protect him. Let him fly and enjoy the man he will become. I am loving seeing my “little boy” become a man.

Unis are not nurturing.

You have got completely the wrong idea of what they are for.

Your OP makes no sense.

Its like saying "I'm worried my DS will not eat healthily - which supermarket will make sure he is buying a balanced diet?"

You could pick the smallest uni in the UK and it won't make a difference if he doesn't leave his room.

It's up to your DC to pick a uni where they feel at home and that provides a course that they want. It's not for you to choose. Help by looking at course details on web sites and visiting/attending open days if they are happening, but the rest is down to your DC.

No uni can make your child leave their room or make friends.

It might be about him finding his tribe rather than being something he isn’t (yet). Cardiff accommodation is relatively cheap and the cost of a house/flat that has a space for mixing and socialising is good value compared to other universities. They also offer quiet and non drinking accommodation.

St Andrews is a small uni that has been very good for my quiet DS. He chose catered accomodation to be more sociable, as it has lots of international students the halls organise many social events especially during freshers week. It tends to have student social life built around student run societies (as its not in a big city with lots of clubs etc) which also suited him. It regularly tops student satisfaction tables so lots like it.
I havent got experience of large unis to compare though.

Even the smallest uni will have thousands of students with 50 plus undergraduates on each course. He will have to interact with people on his course and if he is in residential halls it's almost impossible not to meet people. Encourage him to join a club or society. It's quite hard to completely silo yourself from others at uni.

Whether he leaves the room and makes friends has nothing to do with the university. They might be different sizes but they're all huge institutions with thousands of students. Theres never going to be someone coaxing individual people out of their rooms. It's up to him to join societies, make an effort to get to know people and put himself out there. It can be very hard but it's up to him.