There is a lot to unpack in this statement. First, you should absolutely edit this to change the name and gender pronouns, you are clearly misgendering this person. Secondly, being trans isn't about gender association, it is expressing and living as your gender, period. 'Gender association' implies that there is some true gender rather than what Chelsea Manning has stated and that is very transphobic whether you realize it or not.
> What's considered the current best way to describe this, that Bradley Manning released the documents (past tense) and now Chelsea Manning needs support (present tense), or that Chelsea Manning released documents and now needs support?
The latter. Chelsea Manning released these documents and now needs support. If you are speaking to specific historical information, sometimes you may need to refer to the previous name. However, it is rare to need to phrase something this way and usually such phrasings serve to portray being trans in a negative light.
> The first way feels like it's more useful for expressing the situation to those that lived through it, but may be ignoring the identity of the person in question. Referring to the person through the later moniker in all instances may be confusing to those that miss the change as it happens, but may be less confusing to future generations.
It is not confusing whatsoever. People change names and aliases all the time for a variety of reasons but the world doesn't end and future generations aren't confused as to who someone is. Moreover, misgendering someone isn't just ignoring their identity, it is a slap in the face and challenges the validity of their existence.