Programmers talk to other programmers in terms of functions all the time. Every API you use exposes functionality. If that API assumes some sort of state, that can cause issues for the consumer of the API. It also forces whatever entity is maintaining state be tightly coupled to the consumer and leads to centralized systems.
If the API does NOT have state and instead uses a token based system for authentication and access permissions it is operating in a functional manner. State is maintained outside of the function.
The less coupled that two modules are the more portable that they are. You can bundle up something like the "express" npm package and ship that off to whomever. You can easily build modules on top of an express application by passing the entire app to another module. This pattern has been used to build an entire ecosystem of loosely coupled middleware.
These are not Object Oriented designs. They aren't entities that communicate by sending messages to one another while floating around in some global workspace. They are interfaces that pass state around as arguments to function calls.
Global state is very nicely demonstrated in how modules can be shared between Node and Browser Javascript. What is global? All of the I/O. Files, XHR, mouse clicks, sockets... all of these are the inputs and outputs and all are handled by "window" or "process" or other global state.
Modules can be easily be reused between the server and client if they do not interface at all with any sort of global state.
I seriously doubt it. In order to talk in terms of only functions, you would need to give up identity...because what is identity but not a key for encapsulated state? Without identity, you really are talking with just values, but you have problems describing things with handles. There is no single Bob, just a new Bob who is reconstituted each time you talk about him. Naming anything is weird, and the pure lambda calculus of course avoids it. Most APIs are not purely functional, but somewhat object-oriented (oriented around identity) if only in a few key aspects that are needed to do anything at all.
If you didn't have an identity, then that would be impossible, it is like a superpower where no one could "remember" who you are, and therefore nothing about you.
A UUID is synonymous to state, and in fact, procuring and propagating these IDs would be the main step to implementing state in a pure language.
Take Facebook OAuth for example. A user logs in, is provided with a signed access token by FB, and then uses that token to prove to an application that the owner of the secret key has granted them permission. The owner in this case was Facebook itself.
This can be verified by the server by comparing the:
var expectedSignature = crypto.createHmac('sha256', FACEBOOK_OAUTH_CLIENT_SECRET).update(encodedData[1]).digest('base64').replace(/\+/g,'-').replace(/\//g,'_').replace('=','');
with the signed request signature:
var signature = signedRequest.split('.',2)[0];
and making sure that they're the same.
This way the server never needs to maintain sessions, cookies, or a whole bunch of other crappy, centralized, coupled, insecure methods for building networked software. The server only needs the secret keys of whatever access tokens users might be providing. The access token contains the userId or any other relevant information. If the server needs more information about the user, it can provide the access token to another API that returns more information about the user, again, based solely on the access token, just by passing state INTO whatever system/function/service needs it.
If this server is sitting in front of a database all that the server cares about is what the access permissions are of whatever incoming request it is dealing with. It still doesn't need to maintain state. The database is maintaining state, but the server is just verifying that the request can make the changes to the state of the database.
All with the wonders of functions, modules, and APIs that try to operate without managing their own internal state, which again, is the main feature of functional programming languages.
I'm also not certain why you think this conflicts with the idea of talking "in terms of functions".
Citation needed. I personally don't talk to other programmers in terms of functions, but I use plenty of metaphors and analogies that come with my evolutionary capabilities to use natural language (math, on the other hand, was something I had to learn).