god save the king - including 'rebellious Scots' verse - was written for performance in London theatre as The Bonnie Prince and his Jacobite army marched South, well on their way to take the English capita! Supposed to keep the Londoners in good heart,stop the exodus of fearty people
I can't think of any occasion when people in Scotland would sing Rule Britannia - it's not in our dna! Freedom Come A' Ye perhaps, certainly amongst 'folkies'

(I am old enough to remember when 'the national anthem' was played at the end of (every?) function, cinema, theatres etc - and people all stood! by the time I was third year at school rebels amongst us were refusing to stand or sing - and I joined them. Preferred to sing ban the bomb songs. I've not sung the anthem since, nor stood for it. If at a function where there's a 'loyal toast' - I don't, tho if I am at top table I pass my glass of whisky over a glass of water and quietly say 'king over the water'!