Maybe I'm just a vengeful person, but Regulus' caretaker didn't get punished? At all? She fucked up TWICE! Regulus nearly died because she wasn't watching him properly (and she was explicitly ordered to protect him because the other mansion believes the staff in Ageha's home HATES Regulus!) AND she yelled at and insulted Aleksei who she should be well aware is a national hero because she's not a fucking five-year-old like Ageha. The first is a mistake and she apologized to the head maid, okay, but the second is an unbelievably huge fuck up and she didn't apologize to Aleksei, the head maid had to do it for her. I cannot believe this idiot gets away with this shit scot-free, she should have at least been reprimanded. SMH
I assume she has been reprimanded, but it's been done off pages. After all, her employer is well aware of her mistake towards a national hero and has had to apologise on her behalf. If she hasn't, it's good to remember that the one responsible for that would be her employer who on one hand does not seem to be that wise and on the other likely does not have the means to hire someone more competent (and he only brought one maid so he can't exactly replace her). Also, if anything, her employer was likely pleased that she had pushed for Aleksei to tutor Regulus and may have instructed her to do so. He also should have properly instructed her on how to behave towards him so it's his failure.
I'm not sure how knowledgeable most people are regarding national heroes. The head of servants of a noble household would certainly need to be aware, but even then we see that the head maid did not have the appropriate response since an apology could only come from the master of the house. I imagine most commoners have no clue; do recall the statement "in the empire, nobles are not permitted to refuse" so I'm sure that commoners have no clue what the rules of the aristocracy are.
As for protecting Regulus, that's such a vague task. Is she competent to protect him from poisoning attempts, assassinations and more? How exactly is a single person expected to protect him around the clock with no breaks? When it comes down to it, her employer's inability to hire enough resources for the task is the real culprit.
That's not to say she is blameless but as long as she learns from her mistakes and does her best within reason, there's not much more to do besides instruct her on how to not repeat the mistakes. She's clearly very dedicated to Regulus and she has shown that she's humble enough to self-reflect on her mistakes and apologise. I'd say the only reason she didn't with Aleksei was because the matter was escalated before she could do that.
With all that said, I am a bit worried about her impulsiveness and shamelessness. It seems inevitable that she's going to fuck up again so I can't say I don't understand where you're coming from...