Agree that this would be very difficult to see taking place in a situation similar to the one we have now. SNP politicians are mainly left leaning, many of them likely have doubts about the British monarchy right now. Politicians in the rest of the UK who are just as left wing as many of them, such as Plaid, the Greens, or the left of the Labour party, are broadly republican. They wanted to keep the Queen after independence, but that was in part a political choice in order to avoid losing votes rather than based off of conviction.
The monarchy is popular in the UK, but that is mostly to do with the Queen herself rather than the popularity of the principle. Polls have shown that many British people would be less supportive of it if Charles were on the throne, who is less popular. The idea that offering someone from the continent who is clearly not Scottish or even British the crown would clearly be unpopular with the public. They would likely much rather they stuck with the current Queen instead.
If you want a Stuart restoration, you would likely have to go far back with a PoD which makes Jacobitism deeply instilled within Scottish nationalism, and either makes independence happen far earlier, in the first half of the twentieth century max, in order for it to be an acceptable move to the public. That, or you would need to find a way to rejig the political identity of Scotland so that it becomes particularly rightwing in comparison to the rest of the UK rather than leftwing. And, as others have noted, you would likely need a Stuart who is visibly Scottish, especially in a later independence TL.