That's a common trope, where the only difference between going out and not is just going out...
It's also quite common in more "mature" story to have character developpe their romance normaly.
Seeing the story, author seem to try to make the romance develop "organically".
If you look at all the little things you will see that they are extremely close. You have all the moment were they act a little spoiled with each other, there are moment were they try their best to express themself with the little romance "skill" they have.
Their romance is progressing quite clearly, it's not just going from 0 to 100 in a few chapter because author seem to want to link Yuki's character grow and the romance.
to complement my answer. He is not even a aware of her feelings and quickly dismissed the possibility
Nah, he is just super shy about it, cause Yuki is cute, lovely and gorgeous, but MC is just your everyday normal teen. So he have a hard time dealing with all of this. There are a lot of moment when you see that he understand how close they are.
There is also the fact that his wife have a super hard time understanding her own feeling, so since she dont understant everything clearly they cant have a "yes we love each other, let's marry and have a lot's of kids"