Here to save you lol
https://www.mangago.me/read-manga/totally_captivated_dj_mr_sangchuls_diary/th2/ibx_chapter-2/pg-1/
If you go to this link and go to page number 21. You will find the author's note there.
So she was planning to clarify thier relationship in the side stories but due to reasons I don't know she could not make a story to clarify it.
Hence, she writes it down on the author's note.
Also, there might be a reason why you missed it earlier since the uploads didn't include the author's notes. The new uploads included to notes too.
Hope you find some assurance and have fun rereading with an easy conscience.
Oh yeah. The old man did "sleep" with him but it was non penetrative and that is why mookyul thinks he wasn't cheating on ewon since for mookyul it wasn't sex unless penetration is involved.
It was even implied in the side stories that the old man doesn't like to drill any holes in him.
So that's that
Honestly, I just conveniently get amnesia about them whenever I reread the main story for the sake of my mental peace.

Everytime I'm done reading the main story I come here to reassure myself that the wrinkly old man has nothing going on with Mookyul now sheesh.Why would he even look at someone he brought up sexually wth,Mookyul was also in the wrong too but what could he do,he had no option but to follow the old fart