The Scots and Welsh are British, yes. I do wonder if they prefer not to be called that, though. I don't know their history but I feel like they're only technically British because of colonialism, and maybe they'd prefer to have their own identity in different circumstances.

yeah i feel like regardless of technicalities, in my brain scottish is just scottish and welsh is just welsh. i’d never like, consciously refer to them as british. and obviously irish is just irish but i was never confused on that one