Some people might say that the browser you are using to look at your webapp or ask chatgpt for something is a local-first app ... making it pretty damn popular.
Also I believe the original comment is right as your browser (HTTP) operates fundamentally on a request reply basis. You request resources, you receive an answer, while you are displaying the most recent answer the state on the server might change. You can have a browser that caches the resources for you and only retrieve the new state after for example a timeout or for example a archiving proxy.
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.