The non-military citizens in the group are not breaking any law by possessing, discussing, or even distributing the classified material, as long as they didn't commit a crime to obtain it. It's protected speech, just like when WaPo published the Pentagon papers. However, despite no criminal liability, they could possibly be sued by the government.
On the other hand, the leaker, or anyone with a clearance, cannot legally possess or distribute the documents.
I've also heard that, in recent decades, Federal prosecutors have not brought Espionage Act charges directly against those they agreed were acting as journalists, although they have been willing to try to force them to reveal the identity of their sources. (There are also court decisions limiting "prior restraint" of publication of classified material, e.g. via a court injunction, but that doesn't necessarily equate to prohibiting people from being punished for doing so after the fact.)
My impression is that it's very much a "leak one document, you have a problem, leak a million documents, the feds have a problem" situation wherein they'll happily prosecute people when the situation is mundane enough it won't draw serious scrutiny but when something is a media spectacle they don't tend to go hard except against the initial leaker.
In general distribution of classified materials even those which have already been leaked is technically an offense.
The question is how likely you are to be prosecuted and in general found guilty.
So sharing a photo of a leaked document that was already been made public especially in the press on Twitter is probably ok form a legal perspective (unless you hold or plan to hold security clearance or a federal government job) but being in on it from the get go would likely land you a charge as a co conspirator under the espionage act.
What now?
And this has already been tested in court.
Also not a lawyer, but my understanding is that the Pentagon Papers case was about "prior restraint", meaning the government tried to prevent the Washington Post from publishing the information. They still could have been charged under existing laws on distributing classified information after publishing, the government considered that but did not charge them. And prior restraint is not always prohibited, the courts just decided that in the Pentagon Papers case, it was not appropriate.
Anyone involved in the leak in any way should only be talking to their lawyer right now.
The fact that he's charged with hacking (merits aside) as opposed to leaking is proof that non-military citizens are indeed not breaking the law.
In May 2019 and June 2020, the United States government unsealed new indictments against Assange, charging him with violating the Espionage Act of 1917 and alleging a history of conspiring with hackers.
https://www.justice.gov/opa/pr/wikileaks-founder-julian-assa...
Conspiring to acquire classified information is quite different than merely possessing or distributing it.