"The space shuttle [Discovery] is the Smithsonian's, and any law that suggests the intention to take it violates the fifth amendment on its face — the government cannot take private property."
Well, then it would be Atlantis, which should provide for some nasty fight between space centers...
The nasty bit here is that the Smithsonian is, like the Post Office, a weird amalgam of private corporation and federal department. Its board is selected entirely by the federal government, including VPOTUS and CJOTUS holding positions ex-officio, and the Speaker of the House and President pro tempore of the Senate each appointing three members of their own house.
Of the 17 board members, 10 are currently Democrats, 6 of whose terms on the board will expire before Trump leaves office, and 4 of whose terms on the board will expire before the 2026 midterms. One member is an independent appointed by Trump. CJOTUS John Roberts is nominally independent, was appointed to SCOTUS by a Republican, but, given his voting record on the court is considered unreliable by moderate Republicans, let alone hardcore Trumpists. In any case, if the matter is litigated, he will probably have to recuse himself both from any board deliberations on the matter and from the inevitable case before SCOTUS given his position in both bodies (and this isn't a personal conflict of interest, it's a conflict of interest created by the CJOTUS having a position on the board ex-officio, which a smarter Congress might have foreseen when creating the Smithsonian).
So while the current leadership of the organization
may be able to make a case for any transfer of Discovery being a taking of private property, by this time next year the Smithsonian board will probably just sign over the title. And even the private property case may be weak: Discovery is the private property of an organization that is itself effectively owned by the federal government, so in the end the government would be taking private property from... itself???