In her first life she must've gone through a lot to get herself familiarised with work and gaining his trust and moreover wasn't she too busy to care about it
I understand your point, but sometimes personal life blends with work life. For example, she had memorized his food preferences, which weren't necessarily needed for her to perform her duties,but something she took notice in working alongside him. So with that point I just find it bizarre that she never made note of his distaste for people knowing his preferences or anything else. It makes the character feel similar to the male lead in a way. As they were both preoccupied with surviving that they fail to notice the other. Though the FL's situation was caused by the ML so you can't argue it's the same.
It's kinda crazy that in her first life she never wondered why he acted the way he did and chalked it up to his personality. Like you had to die to realize that he also has some trauma... like you didn't slowly pierce together the pieces before? Granted they are closer in this life than the one before