I understand that the Romans were unable to conquer Scotland so they build Hadrian’s Wall (which explains the survival of older cultures there). But as far as I know they occupied Wales and Cornwall, so how is it that the Celtic culture (language etc.) survived in those places?
Here is the crazy thing about empires vs nation states. In general because empires hold vast swaths of territory. It is very common for them to be somewhat tolerant of the various groups under their control. The goal is wealth extraction not conformity. So if you let the locals keep most of their culture then they are generally more productive and less likely to get uppity.
Nation states are smaller and tend to lean on a cohesive identity to maintain power. So it is much more important for everyone to be the same. Otherwise it could lead to balkanization.