Hope I’m NOT mixing the beginning up with another story I’m also trying to find the name of. 😐
I don’t remember if the human protagonist is male or female, or if the engagement is between a boy/girl or boy/boy.
A man can cross over into the spirit realm and promises a grandchild to be engaged to one of the children(?) of a kitsune(?) woman. He might have brought the child over to visit them before. I think they might have lived in a Victorian style western house, and there might have been a scene outside of the house of a tea party or some such.
There is a time jump and I think the Human pro. can interact with spirits like Grandpa. From here the story starts to get sorta horrorish.
Human pro. helps do exorcisms or something. I think there starts being problems with a spirit/s or Yokai/s having evil intent towards human pro. and human pro. starts having problems from it. I think there’s a dude and girl (who has feelings for human pro.? Might be fiancé?) that help human pro., maybe have them start living with dude to keep human pro. safe.
For some reason I thought it had been one of the works I read by the author of Banana Fish, maybe because it was from around the same era as some of her works or the art reminded me of how her’s looks after California Monogatari an’ stuff?

Since you brought up the possibility of mixing up different stories... Some of this sounds like the short oneshot by Barikios typically referred to as "Yandere Fox Girl". (It was translated anonymously, so it's not listed on MU.)

If that's one of the stories you've mixed together, perhaps it'll help you untangle it a bit?

While it wasn’t what I was looking for, I am interested in seeing what this author has to offer. Thanks anyways. ☺️

I think I found it!! After all this time of looking for it on my own I re-find it AFTER I post something about it.🤦
I think it’s Hyakki Yakoushou; I was probably thinking I was jumbling two separate stories together since I was remembering the storyline concerning the main character with the sixth sense against a story about one of the yokai/non-human thingy that he encounters.
*The mangaka, Ima Ichiko, has some other really great stories as well (family dramadies, fantastical historicals, melancholy contemporaries, supernatural tinged mysteries…)