No one really knows because they won't make the list of items public. It's all based on circumstantial evidence, and the fact that the British Museum has a bunch of stolen artifacts.
Complete BS. The Royal Collection is very public: you can view images of most of the significant pieces on the website: https://www.rct.uk/about/picture-library
Are there problems with how some of the stuff was acquired? Probably. I don't know. But the lazy assertion that their holdings are secret (the things in this exhibition or the collection more generally) is just completely off the wall.
It's fashionable to complain about colonial theft of artifacts. Fine. Please apply the same level of rigor to statements about this topic as you would to statements about technical subjects. Don't spread FUD or try to glamorize your ignorance by saying "no one knows."
"A computerised inventory of the collection was started in early 1991,[28] and it was completed in December 1997.[29] The full inventory is not available to the public"
