But we're not talking an Austrian immigrant to Germany. We're talking about the UK.

The UK wasn't in the Euro and it wasn't in Schengen. These are two of the most visible aspects of EU membership for ordinary people.

The third biggest effect is automatic migration rights. A relatively tiny number of British people have ever moved to the EU. Losing "freedom of movement" is therefore an issue that a small number of people feel very strongly about, but those people were almost always not actually using it. They liked the idea of it, actually doing it not so much. Whether it's language or cultural barriers, Brits just mostly don't do it. Of my group of friends at school, only one ended up moving to the EU (France). All others stayed in the UK or moved to non-EU countries. Moreover it's not like Brits can no longer move to the EU: they can, they just need to get a work visa. This isn't a big deal.

Of those who do though, they were disproportionately represented in media, politics, academia etc. Hence why the Remain campaign ended up focusing on it, even though for the average Brit this was actually pure downside. They didn't want to move to France or Germany, but they had to compete against the millions of immigrants from eastern Europe who were willing to work for pittance.

"Sure, for many this might just be about symbolism and things like access to the world's biggest single market, its regulations etc."

The US is a much more unified single market. At any rate, every country has access to the EU markets, do you think the EU is cut off from the world? It boils down to more paperwork for those outside it, very often deliberately created but useless paperwork designed to annoy companies into not bothering, but it's still possible to sell for those who really want to.

As for the rest, really? The UK is way ahead of most of the EU on environmental issues. Germany especially is a disaster zone. It's a country that shut down nukes in favour of coal burning and now relies heavily on Russian natural gas as a consequence because it doesn't have sufficient LNG import terminals. You know which country is building new nukes, doesn't burn coal anymore, and has LNG import terminals that let it be no longer dependent on Russia? The UK! The idea that the EU is some sort of environmental and worker rights savior is nonsensical propaganda. The EU institutions don't care about the environment, it's just a wedge issue they can use to build up a support base of people who care more about stated intentions than delivered results.

Finally, re: Scotland. The EU is actually a seriously damaging issue for the SNP. They like to use Brexit as a way to attack the English but it poses major issues for keeping their internal coalition together. Effectively the SNP is an alliance of pro-EU leftists motivated by hate of the "Tory English", and the Braveheart contingent who actually want an independent Scotland but are somewhat conservative on social and fiscal matters. What keeps them together is their shared enemy below the border.

The moment the SNP tries to fight a new referendum, even the least canny opponent is going to point out that the SNP is supposedly a nationalist independence party. The EU hates nationalism, it hates independence, and it's not shy about saying so explicitly. The whole idea of it is to get rid of national governments and blend every country into one! So the core idea of the SNP, it's entire stated reason for existence, is to become independent of one union that controls it and immediately rejoin another. When membership was the status quo position they could mostly ignore this contradiction, but if they fight another referendum they'll have to face it and this will pose big problems.

The second problem is the question of whether the EU would even accept them. Although it is possible that the EU would do it just to spite the UK, in theory it faces major difficulties: Spain and other regions would want to block it to kill off Catalonian independence, and Scotland would immediately be in much greater violation of the budget rules than even Greece was. It certainly wouldn't be meeting the stated requirements to join. If it did join it'd immediately become a major subsidy recipient as one of the poorest states in the EU. It would also have to adopt the Euro, which is an unpopular policy with Scots. Would the other members be OK with that? This issue would be brought up in any second referendum and would force Scots and the SNP to face the fact that Scotland has not been laying the financial or political groundwork for independence, even though it could have been.

Honestly a common belief south of the border is that Sturgeon doesn't actually want independence at all. The lack of competence in organizing it is otherwise a bit hard to explain. The status quo suits her very well, actually becoming independent would make it much harder to blame London for everything whilst simultaneously relying heavily on its support.