You left out the most significant part of the 1707 Union which is that Scotland retained its own national church. The Church of Scotland and Presbyterianism has been very important in Scotland's national identity, for a long time absolutely central. Most of the great and good in Scotland today ignore that as it doesn't suit their values. That makes them dishonest, but hey.
Also, sorry about the spelling mistakes in my previous post. It was early morning and I wasn't wearing my reading glasses
I also apologise in advance for a long post, because I can waffle about this topic for ages, but I have genuinely tried to keep this short (my occupation gives me some familiarity with it, also I did learn Scottish history - from an institution, not out of a book).
First, think of a state, say, France. There is an entity we would call the French state, which includes its government. Then there is the territory it controls, which is what we think of as France. Then there is its lawmaking body, whose laws the French state enforces through its territory.
Now, to the UK. In 1707, the Scottish Parliament passed one law dissolving itself, and dissolving the Scottish Crown (ie, the Scottish monarchy / state / government). The English Parliament did the same regarding the English Parliament and Crown. Together they formed a new parliament and Crown of Great Britain (if you want justification for this it says so in the text of the treaty itself and each Act of Parliament). Its territory was the territory of the two previous crowns, ie island and offshore islands of Great Britain and some colonies that had previously been ruled by the crown of England. The point is this - all sovereignty passed from the two abolished Parliaments and Crowns to the new one.
In 1801, the parliament of Great Britain and the parliament of Ireland did the same.
In 1922 the UK lost a portion of its territory to the Irish independence movement who formed their own state, resulting in the current UK borders. That was not a cessation of any union. It was just that the UK lost most of its territory in the island of Ireland to a new state (at the time known as the Irish Free State) which administered laws made by its own parliament. The distinction matters. It meant that the new Irish state wasn't a party to any international treaties, and didn't take on any of the UK's national debt. That's the starting point of any new state, and would be the situation if Scotland became independent and such things hadn't been dealt with in advance.
Back to 1707. Scots law wasn't abolished, and Scotland retained its own national church (states didn't do health and education back then). But that's by the by - the point is that the Parliament of Great Britain had the right to make laws in respect of each and has been doing so ever since, and the king of Great Britain had the right to administer those laws. What "devolution" means is the legal delegation of the right to make laws by the UK Parliament to the Scottish Parliament, and the right to administer those laws in Scotland from the UK Government to the Scottish Government. When the devolved Parliament in Scotland was created, some politician (I think it was Rosanna Cunningham) misled a lot of people by saying that the old Scottish Parliament had "resumed". But in law that's just not what happened, for the reasons I gave above. Legally speaking, the UK Parliament could pass a law abolishing the Scottish Government and Parliament though for obvious reasons it would a crazy thing to try. I am liable to be corrected by any lurking Irish people, but when in 1919 the Irish Dáil was created, it wasn't a resumption of the pre-1801 Irish Parliament and no one said it was. It was an entirely new thing.
You mentioned the United States. That was a bit different - the original 13 Colonies were separate and essentially clubbed together and devolved (if you like) some functions upwards into a federal government but retained a lot of their own administration. Something similar happened in Australia, Canada and South Africa (which is why those places also have state / provincial governments) but without any rebellions. Not the same as the UK though.
I'll make one more point. The UK is FAR from being the only place that includes former independent states in its territory. There is some real Scottish exceptionalism at play here. Italy contains what used to be Piedmont, Venice and Naples. Germany contains Westphalia, some of Prussia, Bavaria and other places. Spain is basically made up of what was Aragon, Castile and Granada. I could go on. Now, you might say that's not the same as they're all Italian, German or Spanish, but in 1926, when the UK was still (just about) the world's pre-eminent power, Scots said they were British. Now the UK is reduced and that identity has changed, but the identity of Scots in 1926 is every bit as valid as the identity of Scots now. It's perfectly reasonable to call the UK a country, and that's how just about everyone outside it (except maybe some expatriate Scots) would regard it.
Sorry, I realise I've gone on for ages but I hope I've made sense.