I was in a very similar situation with my fiancé, not too long ago. BTC was not in question but a home was involved, and I lost big, 175k big. I will not go into a lot of detail. But you seem to have two fundamental questions.

Do you honor the gift you gave her?

Why does she what access to BTC?

I struggled with this first question, more time then I can count in my break up, I gave back a lot of valuable items to my ex when I really didn’t have to (under my own initiative). She seemed to not to even recognize that I was honoring our agreements and seemed not to care. Honestly it didn’t matter what I did, I was a horrible demon like creature that had to go. It was only later, I found out she was dating another guy. :(

But on a personal level I do see this as a question of your character. Do you honor your commitments or not? So if I was in your shoes I would not take the BTC. As I would regret stealing from someone I loved very much at the time. But I would not give her the private keys either.

Now for the second fundamental question -

I assume she wants to spend the large amount of money on frivolous things, because the money is there.

After reading your post (and coming my own jaded experience), I would not give her the private key and would let her sweat. I believe giving into what she wants is a disservice to you and her. She broke your heart and she mishandled the gift you gave her (along with not respecting your effort/time/research into cryptos). As of right now her BTC keys are not of your concern anymore, and has tough as it may seem, I think she will respect you a little more in the end for not being a push over. Besides we all know BTC is skyrocketing and she will be happy she didn’t sell now to buy a pointless gadget. And if you wait you can always revisit this issue in a year or two. Who knows things might change.

CAUTION-

I would caution you that if she thinks there is a lot of money on the line, she might suddenly become very interested in you again with the sole motivation to get access to the account.

TLDR: Her losing her private keys is not your problem. HODL