
I think it's more of a depth perception problem. Having only one eye screws up your ability to judge distances. He thought the door was closer than it actually was, which caused him to miss the handle. And he taps the door before opening it the second time, probably so he can figure out where it is.

Well yes, he was injured pretty bad a few times...
We don't know much about his condition now. Thinking back about the conversation he had in the car with Nanahara he didn't even look for a doctor regarding his eye and get proper treatment. And back then, when he got injured once he used strong painkillers. His body endured a lot and sensei is showing us his scars in this chapter but doesn't show us his right arm. lol .. It's probably me just overthinking but missing the door knot three times almost in a row can't be only an eye issue. I mean, its been 4 years... Just my opinion tho

Maybe it got a bit better with time. I thought his hand was basically paralyzed in the beginning. Also in that chapter they caught that Brother Dude he pushed his head in the sink and their he didn't use his left arm. I am confused now lol
But that this scene here probably really was just there to make Doumeki aware that there is something. That depth perception argument above makes a lot sense.

Of course we can't know for sure right now. But I don't understand why it can't only be an eye issue. He was already nervous due to being in close proximity to Doumeki. Added to his blindness I don't see why it's so strange that he couldn't accurately locate the door handle. Even before that chapter, the author showed us how losing one eye affected his perception. He managed to bump into a door that was right in front of him in an earlier chapter. That's how bad it is. However, we've seen nothing indicating that his arm was permanently injured.
What we know is that Yashiro's right eye is blind and only Nanahara knows that.
After the bathroom scene I'm guessing that something with Yashiro's right arm is wrong too. He kinda missed the door knot or wasn't able to open the door two or three times.
Doumeki noticed something that's why he stood there waiting.
Their whole conversation was painful. :/
And thanks to the scan group for the second part. It was fun to read and enjoyable.