There wont be anything non-photon to observe this universe, but that doesn't mean there's no spacetime, I think.
I think no spacetime is exactly what a universe full of photons implies.

I didn't follow your argument that without matter, there's no space.
Let's just clear up what we mean by "matter"... I would say anything with mass. Things with mass are the only things that experience time, photons do not. A photon travels from the sun to Earth instantly, from the FoR of the photon. It takes 8.5 minutes from our FoR, but not the photon due to time dilation. This can only make sense when we also factor in length contraction... from its FoR, the distance the photon has travelled is zero, so of course it takes zero time.

So if the universe is full of photons, there is no time, and if there is no time, there is no space.

Flat spacetime is a concept that doesn't exist in the universe. Spacetime can only be flat in the absence of mass, and the absence of mass means no time. How can there be space but no time?

I'm probably wrong about quantum information, I can't say I have a good understanding of that. But I don't think I'm wrong about flat spacetime. Although your counterpoint that photons curve spacetime is something I need to consider.