I find it interesting that they are investigating them for treason, rather than something like espionage. I know nothing of German law, but it feels like it would be difficult to prove that they betrayed the country
"§94 Treason
(1) Whosoever
1. communicates a state secret to a foreign power or one of its intermediaries; or
2. otherwise allows a state secret to come to the attention of an unauthorised person or to become known to the public in order to prejudice the Federal Republic of Germany or benefit a foreign power and thereby creates a danger of serious prejudice to the external security of the Federal Republic of Germany, shall be liable to imprisonment of not less than one year.
(2) ..."
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?
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.
"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.
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.
And, in fact, it makes a certain kind of logic. Per dictionary.com, treason means acting to overthrow one's government or trying to harm or kill the sovereign, but it includes giving aid to the enemies of one's government. Revealing where the government is spying on people may in fact give aid to the enemies of the government.
Now, in a free country, that's balanced by the peoples' right to not be spied on by the government. The people have a right to know that the government is crossing that line. (And, in fact, the definition of a free country might be one where the people, rather than the government, are the real sovereign.)
But no, it wouldn't be espionage. Espionage would mean that they were themselves spying, which is not the case.