Any suggestions on how I relay that I’m proud of her without actually saying it?
Great question. My husband's kids (both teens, not BPD, though their mom has traits) both have particular sensitivities to certain words/statements/verbal stuff. I guess everyone does to some degree.
I wonder how it'd go for you to invite hearing from your daughter her perspective on how she did with something, and that could give you a clue as to how to talk about it. For example, she makes a choice you are proud of and are really happy she made. You might ask (in language that sounds like you, and natural, not artificial/stilted): "How was that for you?" or "How are you feeling about how that went?" or "What's your take on how that went down?"
It's possible she could respond with "I felt pretty good about it, I feel like I thought it through ahead of time" or "It was fine, I'm definitely glad I worked hard" or "The first part sucked, but then after I made it through I did OK".
Statements like that would hopefully give you a clue as to what she'd want to hear -- so with the first one, your clue would be "she thought ahead" and so maybe there could be a compliment on "You really planned ahead and it paid off for you". The second clue could be "she worked hard" and a comment could be "I noticed your diligence and effort big-time yesterday". The third clue could be "it sucked but I made it through" and the compliment could be "you stuck with it and persevered... I'm impressed".
My hope would be that whatever language she decides to use about herself could be a clue as to what she's open to hearing.
I tend to do this more with SD13 -- ask her "what's your take on how that turned out" and she'll say something like "it took a while but I'm so excited about it", so my clue is to validate the long time and excitement: "this has been a long time coming, and you stuck with it and are stoked about how it looks." I also am trying to not use the word "but" any more.
So I tend to stick more with pure validation and reflecting back her experience to her. I did say that DH and I were proud of her the other day. I think I need to take a page from your book and preface it with "We don't say this enough, but we're so proud of you". Maybe that's a good balance -- where too many instances of saying "I'm proud of you" send a sensitive kid into overload, but then they're also sensitive to not hearing it enough? So we say it less often (in order to help them stay equilibrated), but "wish we could say it more"?
Sensitive people take some unique care!
Hope those ideas help;
kells76