(speaker here) regarding the limits of stateless apps see
https://driftingin.space/posts/session-lived-application-bac..., the trend is that the more complex your app (think an IDE), the more the "stateless" approach is too slow and breaks down. (Note that what people call "stateless" is not stateless at all; there's database query effects, network effects, session state – and then on the client we have dom effects, reactive rendering and component local state. Modern web apps are actually entirely imperative except in isolated little components where we pretend)
The system we describe in the talk is indeed stateful, but it's worth pointing out that the Photon runtime is referentially transparent in the pure functional programming sense. People think functional programming is about avoiding state and effects; it's not. It's about gaining control over our effects so that we can orchestrate scaled up fabrics of millions of fine grained effects without loss of composition, reasoning or control. This is the promise of modern functional effect systems, and is the underpinning abstraction that powers Photon.