Yes, the estate is part of the National Property Board Sweden (Statens Fastighetsverk), which is a publicly held agency.
In 2009, the government transferred the right of disposal back to the king, in order to prepare a home for the CP couple, but they don’t really own it, only uphold the right to live there
As Haga is one of the Royal Palaces I would imagine that it is owned by the Royal Court but is used presently as a private residence. Actually while I'm typing this, I seem to recall that the Swedish government may technically own the building but the SRF use it- though I may be imagining this or confusing it with somewhere else!
Before Vic and Dan moved in and after the Hagasessorna had left the Palace was used for diplomatic purposes.
I would imagine that the gift of Haga would be comparable to say the Cambridges use of their KP residence or the residence in wirh Mary and Fred reside, where it is "their" property to use privately, but they do not actually legally own any part of it.
I think its very unlikely with Vic and Dan, but I don't think the Swedish Court would allow a historic site to be privately bought by a Royal couple in case of a divorce etc?
Thanks to both of you