I agree with the majority of the things you are saying, however, the distinction between New Atheism and existing secular frameworks, ideals and organisations is the aggression, counterattacking nature that emboldened a callous attitude in it's followers. People of varying religious perspectives were able to participate in processes like the enlightenment and emancipation, and governments formed around that time aimed to replace the power of the church but not humiliate followers.
There are documented posts of edgelords who took that shit too far that illustrated the picture of a fedora wearing edgelord saying things like "oh my science" and trying to get people to abandon their faith, who were not toxic with their faith.
That's what the OP is complaining about, and the response that atheists don't congregate or proselytise is not correct.
No one particularly says "fuck the Quakers and humanists" or "Fuck the UN" because of their secular stance. Secular, interfaith dialogues take place, and instead of respectful inclusion in that, new atheists were more interested in holding up and bringing disproportionate attention to the Finsbury park imam with the hook hands who was preaching all kinds of hate.
Just fucking report him to the cops man. There are many other mosques in London that are basically an apartment over there that some guy runs once in a while for the benefit of the community to get together and celebrate an event, who has a fucking day job.
Or saying that torture was necessary and not even that bad, which is awful for human rights, and then literally throwing in the towel because he couldn't handle it when they did it to him. Abu Hamza