It looks like he's built a little bubble nest. Would this have anything to do with the not eating? I don't think it would, but just asking.
No, it means he's quite happy - happy enough that he's preparing for babies

It doesn't mean he has any babies to take care of, of course, but, needless to say it has nothing to do with his lack of eating.
In fact it means he probably doesn't care about food right now, if he's thinking about babies.
When he's hungry, he'll eat. This is normal and common among new bettas adjusting to their home. He might be picky with his food or he might not be hungry.
There is probably nothing wrong with him, though, even though I don't want to scare you, I have to say that lately I've been hearing more about how bettas with this problem will sometimes not eat for weeks and die...
But he should eat soon. ALL of my bettas did this, all of them eventually ate, and, to boot, now they always JUMP for food when they think they'll be fed! It's really cute to watch.
