I'm also not sure to what extend you can call nodes of an FAI of the same origin that have millions of light years between them the same FAI.

That's a valid point. An AI can rapidly expand across interstellar distances only by replicating and sending out clones. Assuming the speed of light limit, the clones would be essentially isolated from each other and likely to develop independently. So while we talk about "AI expanding through the light cone", it's actually a large set of diverging clones that's expanding. It's an interesting question how far could they diverge from one another.