He feels lucky that he's shifted at this point in his life, and not earlier. He's able to handle it now, and while it bothers him from time to time to have two different set of memories, he works through it the best that he can. While he can see people for who they really are, he chooses not to do anything, no matter who the person really is. He's realized that people treat this situation as a second chance, and most of these people, well they're not aware of who they really are. Why would he want to mess that up unintentionally for someone else? Why would he intervene where it's not his place to do so? People are, as always, in charge of their own lives. Just as he is in charge of his own.
So when he sees people for who they really are, 'hero' or 'villain', he says and does nothing because it's not his place. People take second chances when they can get them, and people can and do change. He's changed enough in the last two years to know this, and all the things that he's gone through, that Bruce has gone through in the past two years alone tell him that the world is constantly shifting. Constantly changing. People will always want chaos and people will always want peace, and sometimes the two combine and sometimes they fight each other tooth and nail. But it's just how the world works.
He knows this isn't Gotham. When he looks at Boston through Bruce's eyes, there is a longing there. He longs for things to be a certain way, he misses his Manor, he misses the real Batcave. He misses the real Wayne Enterprises. Hell, he even misses the Watchtower, but that's not something he'd ever admit to anyone in listening distance. (Because he's a man who likes to work alone, right, he has a character to play up. He's always been doing that. Playing a character. It's what he's good at doing.)
He misses the people who aren't here. He misses Jim, because the other man was as close to a best friend as Bruce got, and there was an understanding there. He misses J'onn, because the martian and him had more things in common than even they wanted to admit sometimes. But he knows that they're most likely around Boston somewhere, they're just not awake yet. And when they do awake, they'll be able to take a second chance, get a life they want, rather than a life of obligation. Maybe, those who are still sleeping will wake up and want things how they used to be, maybe they won't. But that's a decision they have to make for themselves.
He won't be the one to make it for them. He knows better than most what it is like to be forced into doing something that wasn't for him, that wasn't right. He knows relationships he had been through in the last two years, he knows friendships that he's lost because of it. He knows everything has a trial and an error and he is still figuring things out himself. But he's doing it for him, not for anything or anyone else.
So sure, this isn't Gotham. And he's not just Bruce Wayne anymore. But he's making the most of it. It's the least he can do.