The possible explanations you've brought up does make me feel a little better. If she was being strictly monitored by wizards and subdued with magical chains then I wish the author would've written that instead of glossing over it. Hell, to make sure she can never escape why not amputate her? Is it necessary for her entire body to be intact to be transformed into a sword? As for being threatened with her family, I am still reluctant to accept that explanation. They obviously never cared for her, yet she is willing to die for them? Their familial bond is extremely shallow. If they loved and cherished her, I can understand why she'd sacrifice her life for them, but their indifference towards her is only a plot device served to later make them regret mistreating her. This is a very common trope used in rebirth/regression novels.
About the tutoring thing, MC has the reputation of being an incompetent duke's daughter, it's still weird how she even got hired. It's not like she's the only knight around, plus she's only a teen. Well it seems like the ML accepted the MC as tutor because she reminds him of his mom. I really hope this isn't the only reason he would put himself in grave danger. And how is it possible that a prince has never had a tutor up to this point (bruh he's already a teenager. What'd he do this whole time?). Gaining knowledge does not mean contending for the throne. Being a prince comes with responsibilities, even if he doesn't become king he has other diplomatic uses. Only one brother needs to become king, so the other twelve automatically become useless? ALL members of royalty need to be trained to conduct themselves as royalty. And the emperor allows all the heirs to try and kill each other? The nobles are okay with this?? What is the power structure in this universe?? Royalty and nobles dying won't be questioned??? Why does the law even exist...
Also I went digging for spoilers in the novel thread looking for some reasonable explanations to fill in the plot holes. The citizens never knew about her disappearance/the experiments, that's why all the mages were killed by the emperor. She's ruining countless lives by supporting a tyrant for her revenge. Another thing, I still have no idea how the emperor got away with that. A duke's daughter who's also a swordmaster disappeared right after her oath (her fam really didn't give a damn wow) and a bunch of wizards in the castle "went missing". Also OP magic sword appears at the same time. Not sus at all 😐
Here are some other complaints I saw while searching. Her revenge plan in the novel is to use the ML, a royal, to ruin the royal family. If her plan is to ruin them, why is she helping him?? Should she not hate him too? As long as he's alive, the royal family lives.
Another weird detail; ML secretly controlled the empire after the emperor's death. It's hard to believe the genius ML had no knowledge of MC as a sword. Like I previously mentioned, there are a LOT of tipoffs. People talk. He's a genius but not genius enough to figure it out? Or maybe he knew and allowed his brother to use her.
I don't like how we the readers have to come up with reasons to justify the MC's behavior and fill in the plot holes ourselves. It is my honest opinion that the ability of the author is lacking and she just didn't care about these "trivial" details. After all, people are only here for the badass MC and yandere love interest right?
As for the Mary Sue traits, here's what I've found so far. Took control of her family in 2 years despite being unfavored, then left without her family knowing. Also she casually mentions that's she rich as she leaves (did she take it from her family??). She's charming (she is able to make people like/desire her), beguiling (yet she's also an iceberg), "mysteriously beautiful with eyes blue as a galaxy", and is part-fairy. Her fairy lineage doesn't help her at all before her regression despite being able to charm and seduce others. It only comes into play after the regression and tragic backstory has finished occurring. After the regression she has infinite mana, is knowledgeable in every aspect of life due to her 400 years of experience, a master swordswoman as a young girl, etc. She's so Mary Sue she could pass as a middle schooler's self-insert OC.