unwanted, welcome here! You will find lots of supportive people who've gone through very similar things to you.
I see a lot of in there I'm going to pick a few things to address.
I don't know if I should trust her not to lie again.
You cannot have certainty that she won't lie again. I haven't read your back story to see what sort of lies you ran into before.
I can say that many (but not all) "lies" by a pwBPD are following a different mechanism than a 'normal' lie to manipulate somebody you. Instead they are a byproduct of the illness where her feeling RIGHT NOW is the only thing she can experience, (pick one: she loves you, she hates you, she is afraid of you, she is afraid of losing you, etc.), so in her mind, this present feeling is the way everything has always been and the way everything will always be. Consequently, any "facts" which contradict this are re-written.
Something nice you did for her in the past, either didn't happen, or was done for an invented reason to harm her. (If she has painted you black.)
She claims that she's afraid of me and my reactions. This hardly seems fair to me... .[reasons]
Her fear is her feeling. The feeling is real. Whether the feeling is justified or not doesn't matter. The feeling is real. If you try to tell her why the feeling isn't justified, you invalidate her and make things worse.
There is nothing about feelings that are "fair" or "justified". That's not how they work.
Is there anything I can tell her or talk about to make her feel better?
You can be kind and validating, which can influence her feelings. (Read the Lessons in the sidebar ----->> >>
However, nobody can "make" another person feel anything. That's not how feelings work.
she's saying that she's "no longer afraid of me" due to my reassurance so that she can patch things up and act like nothing's wrong again, all while resenting me behind my back
I'm sure her feelings and motivations are kinda confused... .but you have very little influence over them. You will do much better focusing on her behavior than what she might be thinking.
How do I know if the relationship is irreparably damaged, meaning that she can never feel "safe to tell the truth" around me again?
You don't know. I would say that pwBPD are VERY capable of turning their feelings around on a dime... .and then acting like they never had contradictory feelings in the past. It is crazy making. It also means that she is very likely to say she will "Never feel/do X again." and then say she will "Never do the exact opposite again." And bounce back again.
Believe that she feels that way... .at that moment... .don't believe that it is forever, even if she says it is.
Do we both need to learn how to trust one another?
I think so. Focus on being trustworthy. Especially according to your own values, not just in what she asks/demands of you. She isn't likely to be good at asking for what she really wants/needs directly.