I started to sit down and write a long diatribe about all of the historical errors in this book-- errors of history, not just anachronisms. Then I decided that I would just bore anyone who read that wall of words. So this is the short version.
If you don't mind the fact that the author writes a Note at the end to mention that she made up Ann of Savoy and fails to mention that she also made up a lot of other stuff including the fear of a curse against England because George III went mad, then you might be all right with this book.
She does get the Jacobite heir at the time wrong-- it was Charles Emanuel, King of Sardinia (Savoy was a Duchy which became part of the Kingdom of Sardinia in the 17th century), not his brother Victor Emanuel. Charles had abdicated Sardinia but kept the personal title of King some years before the last legitimate Stuart died and the right passed to him by both descent and the will of Henry, Cardinal called Duke of York.
To be fair, the PC attitudes that other people complain about are not out of period. This was a time when people where examining what liberty and rights of man (and even women) meant.
However, the idea that the hero could recognize an accent as from the south in the USA based on his father having spent time in Georgia "in his youth" is entirely too much for me to swallow.
So no, this isn't a very good HISTORICAL mystery. Nor is it terribly good mystery.
If the reader is interested in a contemporary mystery that also works in the death of the Duke of Cumberland's valet, I would suggest Kingdom of Lies by Lee Wood. I recommend the Audible download.
And in case anyone cares (or is still reading), there was an alliance between Goditha Price and James, Duke of York, as mentioned in the Author's Note, but without children-- the Stuarts weren't shy about claiming their children by mistresses so there's is no conspiracy there. Goditha died young, unmarried and childless before James took the throne as James II. The records that remain of her (Pepys, MEMOIRS OF THE COMTE DE GRAMONT. and the Earl of Rochester) are not kind.
I think that making up half royal children for Americans to claim descent from is almost a cottage industry.