Scotland isn't a principality - it is a Kingdom!
One of Prince Charles' titles - as the heir apparent is - Prince and Great Steward of Scotland which suggests that it is a Principality.
Note that the Queen isn't the Queen of England or of Scotland but only of the United Kingdom of Great Britain and Northern Ireland.
This has some information about the title and the time when Scotland was both a kingdom and a principality - the latter only really ending in 2002
https://en.wikipedia.org/wiki/Prince_of_Scotland
Principality of Scotland
The title of Prince of Scotland originated from a charter granting the Principality of Scotland to the future James I of Scotland, the then heir apparent, on 10 December 1404, by Robert III. During the reign of James III, permanency was enacted to the title. The designation "Principality of Scotland" implied (and implies) not Scotland as a whole but lands in western Scotland, in areas such as Renfrewshire, Ayrshire and Kirkcudbrightshire appropriated as patrimony of the Sovereign's eldest son for his maintenance.
In modern times, the Prince remains paramount superior in these lands (whilst The Crown serves this role in the rest of Scotland). The Abolition of Feudal Tenure etc. (Scotland) Act 2000, however, abolished most remaining feudal duties and privileges attaching to the Principality,[4] leaving the Prince's status as mainly titular. Prior to the 2000 Act the Principality was entirely feued out to tenants and brought in a small income. All title deeds in Ayrshire and Renfrewshire required to be sealed with the Prince's seal. Revenue gained from feudal dealings were counted as income for the Duchy of Cornwall, a more substantial estate held by the monarch's child who is heir apparent.[5][6]
