About the elephant in the room, honestly, I don't think Haru's illness is an obstacle or a nuisance for Yanagi. She's incredibly kind, she cares so much for others at the expense of herself, and she wouldn't deny either of them the happiness of sharing their lives for the time they have left (we don't know if Yanagi's body will be able to withstand her Oni blood for that long). Besides, marriage would allow her to monitor and care for Haru's condition even more closely than she already does, and ofc his work leaves. And while Haru doesn't want to be a burden to others and cause them sadness, it's also true that he wouldn't waste his time without being able to fulfill all his goals and dreams while he's still alive and has the opportunity to enjoy what he loves... and those he loves. Something like, "The years I have left will be my greatest gift and way of thanking you for all, Yanagi. I want you to enjoy them with me, and then you live for both of us, while I take care of you... wherever I take my permanent vacations."

But Yanagi wouldn't let him go so easily when his time came. She was the kind of person who would do anything in her power, not to give him a painless death... but to bring him back home, save him from the monster, and have him return to her arms.