I was going to comment basically this. The construction isn't forever. Having been through this as the neighbor, I do understand that living next to construction isn't something you agree to when you move in. So you could acknowledge that the noise is an inconvenience to him, at least. You are right you have done everything correctly. But that doesn't mean that the noise, at whatever time of day, isn't an inconvenience. So just try to remember and have some compassion that he's living next door to a construction site right now, and it may not be that pleasant for him. I wouldn't expect that he will continue to complain after it's over.

Regarding the music, that's a little much. If I'm working from home, not only do I have to listen to construction all day while I'm working but now the person's music too?

Just saying, this is a little bit of a situation where you both are right. You are right that you have gotten all the permits and permissions to do the construction, and he's right that it's inconveniencing him. At a certain point you can only do what you can do.

You're going to live next to this person for a while, so I don't think an F U attitude is going to be productive. Someone else suggested reminding him when you will be done. I'd just stick to that. "I apologize for the inconvenience, we will be done by X date. I appreciate your patience." I think that's your mantra.

(And I would ask the construction workers to turn down or nix the music.)