As usual when comparing different legal systems it gets muddy. I guess what you're having in mind is more like "Hochverrat" (high treason).
An aside: what are the connotations of "treason" and "treachery" in English? Is treason the criminal act against your country and "treachery" more personal, betraying a friend?
"treachery" is the more general term, that would apply to anything from personal betrayal to particularly underhanded business dealings. It's roughly equivalent to "betrayal", though more emphatic.
"treason" can technically refer to the same thing (you could say "this is treason" to refer to some personal act of betrayal, though it would come across as hyperbole), but in practice it almost exclusively refers to the crime.
An opinion regarding usage from a native speaker, here: it might for instance be considered treacherous to lure the King into a forest where he may be murdered, in return for a rich reward from a pretender to the throne; but merely supporting the pretender in hopes of a reward, even to the point of secretly betraying the King, might in other circumstances be plainly and distastefully treasonous without evoking the same connotations as treachery.
There are archaic British legal meanings of the word treachery which might parallel your distinction of Landesverrat and Hochverrat, I am not sure. But only lawyers on the Commonwealth side of the fence would likely understand that meaning.