Bushnell did, in fact, call herself Lilly with she/her pronouns on multiple accounts, especially ones that weren't as easily linked to his public identity, a very common trans practice for someone who isn't ready to come out (seriously, spend an hour browsing any forum of trans people and you will find half of them are in this exact situation). Why would someone not want to come out? Lots of reasons, including being in the US military a fucking awful place that statistically white transfems in the US are over-represented in. Though the majority of them do not come out while they are enlisted.

Why not come out at the time of death? That's a ridiculous thing to expect. usually being closeted is a key part of what would make someone feel miserable enough to actual kill themself. It's not like killing yourself actually saves any lives from the military's evil, nor does it move the US population to do anything. This was, while a powerful political statement, ultimately just a suicide. There are way more effective interventions an enlisted person who was not afraid of death could undertake, Bushnell chose a suicidal, and only self-harming one. Also, stating your legal name and enlistment status is part of the statement, not evidence of not being trans. In fact, using that moment to "come out" would very likely have the effect of undermining the political statement. It becomes: Bushnell killed herself because she was an unwell trans person, and not because she was horrified at her participation in the genocide of Palestinians.

That being said, no, we do not have any "proof" that Bushnell was a trans woman. What we do have clear evidence of is that Bushnell used the name Lilly, and used she/her pronouns. Bushnell also used the name Aaron and used he/him pronouns. That is definitionally trans. Whatever label Bushnell related to, we can't know. But we know he used the name Aaron, and we know she used the name Lilly, so Bushnell is, by all evidence, trans.

The thing is, even though there is evidence of both identities, because of cis-centric and transmisogynistic thinking, it is only acceptable to some people to use the cis-coded identity, and is somehow portrayed as a violation of Lilly's autonomy to use the trans one. But both of them existed, and both of them were used by Bushnell. So why is only he/him and Aaron acceptable? And why would cis men feel comfortable coming online and saying that someone who uses two names, and two sets of pronouns (which is trans even if not a trans woman, because, remember, there are more ways to be trans than one, and using cross-gender pronouns, even if you also use the pronouns you were assigned at birth is still trans) is not trans because there's no proof. Only your assumptions about Lilly/Aaron are correct, even though they rely on ignoring a bunch of evidence, because you are a cis man that assumes cisness as the default.