I think she was one of the few people to be exempt from laws as well- abroad she had diplomatic immunity and at home she had sovereign immunity, since all punishments are passed by the monarch.

For Charles III it’s the exact same situation

She ceased to be a British citizen upon her coronation (the monarch is specifically not a citizen), so she wouldn’t have been entitled to one.

If a monarch hypothetically fled or was deposed, they would legally be stateless.