Scots are not Anglo-Saxon, but if you want to change history and genetics that is fine by me.
As long as I can call you German.
Die Franken? Or the Flemish? Well, they were certainly Germanic. But that is long, long ago. And anyway you speak English, and language is the dominant feature of any culture which distinguishes it from all the others. The French don’t speak German. And you have the English Queen. Normandie is not represented in the Bundestag. France and Germany are not as far apart as history has made them out to be, but to an outsider, the difference is clear. No doubt the Bretons are not Provencale, or vice-versa, and the Scottish are not Saxons, but Breton and and Provencale and Alsacien are all French, and English and Scottish are all Anglo-Saxons: common language, common country, common Queen, common government, common concepts of law (if not the same laws).
The Breton are Celts, but they’re French.
The Scottish are Celts, but they’re Anglo-Saxons.