Another divisive topic. I would certainly address a Scottish person as Scottish and not British. Just as I’m Irish and not British, although that is a different thing altogether being from N.Ireland.
I used to open banking products as a job and never had a Welsh person declare their nationality as British, very few Scots would’ve said British and the majority of people in England declared themselves English. Anyone in N.Ireland was always just awkward 
Obviously this is just my experience, and people on the forum have their own views and opinions on their own nationality. I’m certainly not going to dictate what they are.