I saw your previous questions as well, but I was hesitant to respond since this isn’t exactly my usual area, but given the lack of answers, hopefully I can help out.

As you say, there are really three languages in Scotland. "English spoken with a Scottish accent" (or really several accents and registers) is probably what most people understand by “Scottish”. There is also Scots, a Germanic language closely related to English, and Scottish Gaelic, which is part of the Celtic branch of Indo-European (related, more distantly, to the Germanic branch of IE).

Europe used to be full of Celtic languages, especially Gaulish in what is now France, and Galatian in what is now Turkey. In Britain, Pictish was most likely also a Celtic language. By the time the Celts are mentioned in the written record by the Greeks and Romans, there were distinct branches of Celtic languages - continental (Gaulish and others), and insular (spoken in Britain and Ireland).

The insular branch also developed into what linguists describe as “Goidelic” and “Brythonic”. Basically, Gaelic in Scotland is the modern form of one branch Goidelic, which is itself one branch of the Celtic languages that used to be spoken all over Europe.

In the 5th century, the Roman Empire withdrew from Britain, and speakers of Germanic-languages from the continent began settling there. Whether this was an invasion or migration is still kind of a contentious question - see this discussion of the Angles, Saxons, and Jutes by u/BRIStoneman from a few months ago, for a brief overview. In any case, Goidelic-speakers were pushed further north, and Brythonic speakers were pushed south and west, where their languages developed into Cornish and Welsh, and Breton too - some crossed the channel to Gaul (i.e., Breton isn't descended from continental Gaulish, the Bretons arrived later after Gaul was already Romanized/Latinized).

The new Germanic inhabitants spoke West Germanic languages, which is now often described as "Anglic", as a catch-all term for the various dialects of Old English that developed in Britain. The ones that settled in the north spoke Northumbrian, while in the south they spoke Mercian, Kentish, West Saxon etc. There was another wave of Germanic settlement starting int he 8th century, when Danish and Norwegian Vikings showed up and conquered some of northeastern England (the "Danelaw"). They spoke dialects of Old Norse, which was part of the North Germanic branch rather than the West branch (somewhat comparable to the difference between Goidelic and Brythonic).

The Old Norse spoken in the Danelaw affected the Old English dialects to the south but it had a major effect on nearby Northumbrian. The Vikings also ruled the Hebrides, Man, and parts of Ireland, so Old Norse also had an influence on Irish, Manx, and Gaelic.

All of the Old English dialects were affected again by the Norman invasion from France in 1066. The Normans were originally Vikings from Denmark, but they had mostly lost their own language and adopted Latin-based French. We now describe Old English as evolving into Middle English following the massive changes that occurred after the introduction of Norman French in the 11th century.

Northumbrian English was influenced by Norman French too, but not in the same way. By that time, there was already a distinction between the Northumbrian spoken in England and the Northumbrian spoken in Scotland. Up to the 10th century, the lowlands of modern Scotland were actually a part of England (whether the Kingdom of Northumbria, or a unified Kingdom of England), but in 970 the Scottish king Kenneth III conquered the northern part of Northumbria, a.k.a. Lothian, where Edinburgh is located. This division was cemented after the Battle of Carham in 1016. Lothian north of the River Tweed was integrated into Scotland, the kings began to reside in Edinburgh, and they adopted the form of English that was spoken there. South of the Tweed, Northumbrian English continued to develop into the modern Northumbrian dialects.

The Kingdom of Scotland interacted more and more with the Norman English kingdom to the south. Anglo-Norman settlers and traders migrated to the lowland towns and cities, and the Scottish kings wanted to be included in the French-speaking Anglo-Norman cultural sphere. They even intermarried with Anglo-Norman royalty. So the Scottish version of Northumbrian English was also influenced by the Anglo-Norman of the south and experienced many of the the developments that led to Middle English in the south, while also being influenced by the neighbouring Gaelic speakers. Northumbrian became Early Scots, then Middle Scots, and the modern Scots of today.

Medieval Scottish people began to distinguish between the Lowlands, where people spoke English, French, and Scots and were culturally part of the French "feudal" world; and the Highlands, where people spoke Gaelic and the culture was more rural, agricultural, and dependent more on clan kinship than feudal relationships. There was also a third cultural sphere out in the islands, which remained connected to the Scandinavian world.

As for how Scottish nationalism developed out of these distinct medieval worlds, I would have to leave to someone with more expertise in early modern Scottish history...but hopefully this helps explain how Scotland came to have three different languages: Gaelic, from the Celtic branch, and Scots and Scottish English from two different branches of Old English.

Sources:

Katie Wales, Northern English: A Social and Cultural History (Cambridge University Press, 2006)

Charles Jones, ed., The Edinburgh History of the Scots Language (Edinburgh University Press, 1997)

Donald MacAulay, ed., The Celtic Languages (Cambridge University Press, 1992)

A.D.M. Barrell, Medieval Scotland (Cambridge University Press, 2000)