All but one of the charges are for espionage, a crime the Obama Justice Department decided they couldn't charge against journalists, whether USA citizens or not. This was called the "New York Times Problem". [0] Espionage, since it is a "political" crime, also wouldn't sustain extradition from UK.
The 18th and final "conspiracy to hacking" charge, tacked on to give the UK judges (who should have thrown this case out years ago) a fig leaf, pretends to be of a different nature, but it isn't really. This is the charge for which notorious sociopath, conman, fraudster, and convicted pedophile Thordarson provided the supporting testimony he has now recanted. [1]
The bastards had hoped to bolster a very particular interpretation of a chat log with Thordarson's now-recanted testimony. That interpretation is now very weak. First, they can't actually prove that "Nathaniel Frank" was a pseudonym for Assange. Who's to say it wasn't a pseudonym for Thordarson? In addition, although it is the prosecution's theory that it was possible to crack a password given the partial hash Manning had, testimony before the UK court has contradicted that. [2]
IANAL, but my observation of USA court proceedings leads me to suspect that your question about conspiracy has no definite answer. Conspiracy is always a discretionary charge, which makes sense because there is no victim and no harm. "Discretionary" is nearly synonymous, in this context, with "political", which quality of espionage charges typically excludes extradition. It's often used against criminals who have been careful to leave no evidence of the underlying crime. It is also used to bully innocents without evidence of underlying crime.
Prosecutors in normal criminal cases don't push conspiracy as far as they theoretically could, because normal USA juries don't have infinite patience for pursuing the worst possible interpretations of inconclusive evidence. "National security" cases, however, aren't heard by normal juries. Usually some pretext is found for excluding a jury trial altogether, but when that doesn't work they rely on the TLA-friendly hang'em-high juries found in the Eastern District of Virginia where all these cases are tried.
However, this case isn't currently being tried anywhere in USA. Right now it's a UK extradition case. In such cases justice should override deference to zealous prosecution, as the same judge's previous ruling with respect to squalid USA prison conditions acknowledges.
[0] https://www.washingtonpost.com/world/national-security/julia...
[1] https://www.wsws.org/en/articles/2021/06/28/assa-j28.html
[2] https://www.computerweekly.com/news/252489645/Forensic-exper...