Are you suggesting that AIs would get bored of exploring physical space, and just spend their time thinking to themselves?

I'm suggesting AI's will largely inhabit the metaverse - an expanding multiverse of pervasive simulated realities that flow at their accelerated speeds. The external physical universe will be too slow and boring. I imagine that in the metaverse uploads and AIs will be doing everything humans have ever dreamed of, and far more.

Or is your point that a hyper-accelerated civilisation would be more prone to fragmentation, making different thought patterns likely to emerge, maybe resulting in a war of some sort?

Yes divergence or fragmentation seems in the cards so to speak because of the relative bandwidth/latency considerations. However that doesn't necessarily imply war or instability (although nor could I rule that out).

If I got bored of watching a bullet fly across the room, I'd probably just go to sleep for a few milliseconds

Watching the real world would be just one activity, there would be countless other worlds and realities to explore.