[Rainbow Six]

The most logical reason I can come up with is not dissimilar to what happened IRL during Indyref 1 in 2014, during which the SNP policy was that in the event that they'd won the referendum and we'd achieved independence we'd have followed the Commonwealth model and Queen Elizabeth would have remained the Head of State. Ultimately it's realpolitik - not all Independence supports are republicans so for the SNP to openly come out as pro Republican was - and still is - deemed likely to cost votes. Probably a lot of votes.

So if the Twilight 2000 SNP are trying to act as a legitimate and democratic Government with one eye to the future then there's a case for using the Royal prefix - I could see the SNP leadership plying this sort of line: 'we've been abandoned by the Government in England so we're doing what's best for Scotland in the meantime but we're still loyal to the King - look, our army is even called the Royal Army!'

In other words, they're declaring independence from His Majesty's (British) Government but not His Majesty, who in addition to being the British Monarch is also head of the Commonwealth, which gives a bit of wiggle room.

But it's a big stretch. As a Scot, I think in a T2k scenario the SNP would declare a Republic in a heartbeat, so I don't buy it personally, but I think it's a lot more realistic than a possible Stuart restoration.