Doubt E&J are paying rent to H&M as Frogmore Cottage is owned by the Crown Estate.
It probably is just insinuated by media that H&M are subletting imo because it makes a better story
They were the previous tennants and now E&J are
it's probably not very different from your regular rental: the landlord owns the building, you as a tennant can put your own furniture in it
From sussexroyal website with regards to ownership of the property
https://sussexroyal.com/funding/
How was the Official Residence of The Duke and Duchess of Sussex (Frogmore Cottage) funded?
The refurbishment of Frogmore Cottage, the Grade-2*listed*building in Windsor Home Park was funded by Her Majesty The Queen through the Sovereign Grant, reflecting the Monarchy’s responsibility to maintain the upkeep of buildings with historical significance (see above). Expenses related to fixtures, furnishings, and fittings at the official residence – which is owned by Her Majesty the Queen – were funded privately by The Duke and Duchess of Sussex. As stated on*The Official UK Government website:*“The occupied Royal Palaces are held in trust for the nation by The Queen as Sovereign. Their maintenance and upkeep is one of the expenses met by the government in return for the surrender by the Sovereign of the hereditary revenues of the Crown (mainly the profit from the Crown Estate). The Sovereign Grant will allow the Royal Household to set its own priorities and thus generate economies. The occupied Royal Palaces are:*Buckingham Palace, St James’s Palace, the residential and office areas of Kensington Palace, the Royal Mews and Royal Paddocks at Hampton Court,*Windsor Castle and buildings in the Home and Great Parks at Windsor.”