The Queen is the only person who isn’t liable for any tax in the United Kingdom. Important point to note, she pays Income tax on a voluntary basis. The monarch is also exempt from capital gains tax and inheritance tax so we can assume that almost all of her estate (including jewellery) will be inherited by the Prince of Wales and in due course by the Duke of Cambridge etc.
The reason why the Queen can inherit and pass assets tax free is to ensure that items associated with the Crown do not need to be sold to cover inheritance tax.
On that basis she has no need to shield assets such as jewellery within Trust structures or the Royal Collection. I do not know on what basis you assert the Queen treats her personal jewels as state property, I know of no evidence of this and for her to do so would be both bizarre and illogical. She loans items to family members because it is the entirely logical thing to do, to gift items would not only deplete the Royal Family’s collection but create an inheritance tax nightmare for the recipient.