I just finished Romantic Doctor Teacher Kim and one of the things I really liked was the romance between Seo Jeong and Dong Joo. It wasn't the main focus of the series, it was sort of in the background but not forgotten? And because it wasn't the main focus there wasn't much in the way of relationship drama, we just got to see them flirt and fall for each other and support each other. And the other characters around them saw it too, there's a moment between Teacher Kim and Nurse Oh where Teacher Kim says something along the lines of "do you think I could have stopped her?" (from entering the quarantined ER) and nods his head towards Dong Joo, and they share a knowing smile. I just love that scene for some reason.

I don't necessary need recommendations to be medial dramas (it seems like most of the recommendations on the RDTK page are other medical dramas), I just want something with a similarly compelling sort of "found family" with a drama-free romantic side plot, if such a thing exists? 

Maybe try Drama Lets Eat, it is slice of life with focus on character friendships the romance comes into play much later but it's very lightly building but not the main focus of the drama.