general relativity - Do photons bend spacetime or not?

I have read this question:

Electromagnetic gravity

where Safesphere says in a comment:

Actually, photons themselves don't bend spacetime. Intuitively, this is because photons can't emit gravitons, because, as any massless particles not experiencing time, photons can't decay by emitting anything. The latest theoretical results show that the gravitational field of a photon is not static, but a gravitational wave emanating from the events of the emission and absorption of the photon. Thus the spacetime is bent by the charged particles emitting or absorbing photons, but not by the photons themselves.

If photon can bend spacetime how does it exchange graviton?

Is there experimental evidence that massless particles such as photons attract massive objects?

where John Rennie says:

as far as I know there has been no experimental evidence that light curves spacetime. We know that if GR is correct it must do, and all the experiments we've done have (so far) confirmed the predictions made by GR, so it seems very likely that light does indeed curve spacetime.

Now this cannot be right. One of them says photons do bend spacetime, since they do have stress-energy, but it is hard to measure it since the energy they carry is little compared to astronomical body's stress-energy. So they do bend spacetime, it is just that it is hard to measure it with our currently available devices.

Now the other one says that photons do not bend spacetime at all. It is only the emitting charge (fermion) that bends spacetime.

Which one is right? Do photons bend spacetime themselves because they do have stress-energy or do they not?

Answer

Classical electromagnetic fields carry energy and momentum and therefore cause spacetime curvature. For example, the EM field around a charged black hole is taken into account when finding the Reissner-Nordstrom and Kerr-Newman metrics.

The question of whether photons cause spacetime curvature is a question about quantum gravity, and we have no accepted theory of quantum gravity. However, we have standard ways of quantizing linear perturbations to a metric, and reputable journals such as Physical Review D have published papers on graviton-mediated photon-photon scattering, such as this one from 2006. If such calculations are no longer mainstream, it is news to me. Given that photons have energy and momentum, it would surprise me if they do not induce curvature.

I also note that the expansion of the "radiation-dominated" early universe was caused by what is generally described as a photon gas and not as a classical electromagnetic field. So the idea that photons bend spacetime is part of mainstream cosmology, such as the standard Lambda-CDM model.

Finally, the idea of a kugelblitz makes no sense to me unless photons bend spacetime.

So in Rennie v. Safesphere, I am on the Rennie side, but I look forward to Safesphere defending his position in a competing answer.

Addendum:

Safesphere declined to answer; in a now-removed comment, he said that knzhou’s answer explains the disagreement. I don’t agree. I disagree with knzhou that “bends spacetime” is vague. It is commonly understood by most physicists to mean “contributes to the energy-momentum tensor on the right side of the Einstein field equations”. And most physicists believe that real photons do exactly this, for the reasons that Ben Crowell and I have stated.