I can browse my private my-site.html perfectly without ever having a network adapter in my device. Now granted some modern webapps (chatgpt) are not designed to operate locally, but there are plenty of webapps that work fine from local storage.

A browser is (in my definition) a tool to display what you call a websites, usually a collection of html/css/js resources. One of the options is to retrieve the resources through the network, if you want the latest news for instance. But it is not required and that makes it local-first in my view. I don't think local first means the app can not connect or sync with a remote server.

In the same way as saying we live on earth doesn't mean we are not in space, earth is in space and we are on earth. It is not mutually exclusive.