Honestly, my main problem with Myne right now is that she just... doesn't realize how important she is. Knowledge is power, and she knows far more than practically everyone here, aside from unique in-setting elements. She has all that power, but doesn't wield it. She's even practically given up on her one goal of becoming a librarian, seemingly content to be consumed without doing anything to fulfill her dream aside from introducing paper to Europe much earlier than normal. If she desired it, truly desired it, then she would do whatever was necessary to achieve her dream, damn the consuming, damn the nobles, damn it all. The knowledge she has could fetch a great bargain to the right parties, as demonstrated in this very chapter. She could progressively sell those secrets, gaining enough money to purchase the mana absorption thingies while simultaneously elevating society to make it possible for her to become a librarian.
Alternatively, she could make the contract. Become a noble's wife, but leverage her knowledge to have a favorable deal, and probably become the dominant partner, so to speak. She probably could take her family with her too, if she leveraged what she had well enough. From that position of power, she could wield her knowledge far more effectively, guiding society in the right direction, while opening up the possibility to, of course, read more books.
With great power comes great responsibility, yet she is shirking the responsibility to massively improve the standard of living in what amount to the Dark Ages. Apathy is Death, and she has given up on her future, and become apathetic. She's practically dead already, and I think Frida can see that too.
Frida, despite the whole "loves money as much as Myne loves books" thing, legitimately cares for her friend. She's anguished at the way Myne is taking this, and it shows in her face. How would you feel if a dear friend decided to just... give up on life, even when there were ways to live for decades more? Probably bad enough to react the way Frida is.
tl;dr: Myne is a fool for giving up on everything she can do, and Frida is hurt by that.