And here I thought I was the lone voice in the wilderness. From Roy Fielding's original paper:

The client-stateless-server style derives from client-server with the additional constraint that no session state is allowed on the server component. Each request from client to server must contain all of the information necessary to understand the request, and cannot take advantage of any stored context on the server. Session state is kept entirely on the client

I've heard enough verbal gymnastics to fill a book trying to excuse how modern web apps aren't violating this condition.

Not alone. I find the problem most people have is no suitable example they can think of. The examples we have online are "starbucks as REST", etc. A better example is the greatest REST client ever made: the web browser. When Facebook updates their "app", I don't even need to restart my "client" to get the updated features. These days I start all "REST: you're doing it wrong" conversations with this.

Yes REST tends to mean "web API you don't hate" or "web API written less than 5 years ago" and is heading towards just meaning "web API".

It's an industry cycle. 15 years ago it was "XML all the things!"