The court is faced with an extradition request, which will hinge on questions such as: are the charges well laid out and supported? will the defendant get a fair trial? and does this fit within our extradition treaty?
That second point - getting a fair trial - is heavily undermined if there is evidence the US government has privileged information that came from spying.
> The German intelligence agency used the selectors to surveil telephone and fax numbers as well as email accounts belonging to American companies like Lockheed Martin, the space agency NASA, the organization Human Rights Watch, universities in several U.S. states and military facilities like the U.S. Air Force, the Marine Corps and the Defense Intelligence Agency, the secret service agency belonging to the American armed forces. Connection data from far over 100 foreign embassies in Washington, from institutions like the International Monetary Fund (IMF) and the Washington office of the Arab League were also accessed by the BND's spies.
[1] https://m.spiegel.de/international/germany/german-intelligen...
In reality they seem to be somewhat competent at some things, and reports that they do indeed successfully surveil foreign embassies seem to be true.
Context matters.
Friendly countries spying on each other is super common. The US bugged Angela Merkle's cell phone! We do this. Everyone knows we do. They live with it, because they spy on us, too.
For good and ill, this sort of thing has been considered playing by the rules for decades. You can compare the response to the Russia assassination campaigns on British soil, which (when too public to ignore) created a big public response because that sort of thing was considered out of bounds previously. And the response to American kidnap-and-torture plots in Europe.
That's not to say we don't catch, try, imprison, and deport spies in the US and other countries do the same against us. But this is all part of a decades-long iterated prisoner's dilemma about what the "rules" are in international espionage.