Responses
Spoiler
She does go through an existential crisis which made kael very anxious because she looked like she had no soul. It doesn't really last long because she started to see kael's feelings for her. And Helios also helps her by talking with her. And about the illness, in previous life she didn't bother to take care of herself after kael died. So she became sick. So she won't get sick this life.

Not directly related to recent chapters but Hestia might be struggling a lot mentally, I think a reason why she is so obsessed about Helio and Diana apologising is because she desperately needs a goal to keep going and distract her (obviously it's also because she cares for Kael a lot and wants the best for him too, both can be true at the same time). just re-reading the manhwa and realising how much Hestia was struggling in her past life mentally, she thought she would be able to leave as the story ended but realised this is her new life now and Her physical body deteriorated too. That's an incredibly difficult situation for anyone. And while Kael definitely got her help in his mental issues, Hestia is just ignoring her own issues and fears and using her goal of helping Kael and just general workaholic tendencies to distract herself. There is also the physical illness she will most probably end up having again if the future repeats itself, yet for someone as capable as Hestia she is still ignoring that problem, makes everything almost feel deliberate.
Kael has certainly noticed that she herself might have some struggles she might not be open about. Maybe he will be the one who helps her this time.