Is anyone aware of a concise review of the experimental evidence of the nature of the gravitational field due to an entity in spatial superposition?
Some of the experimental evidence for general relativity can be found at
https://en.wikipedia.org/wiki/Tests_of_general_relativity and there is no experimental evidence that contradicts this except for phenomena commonly attributed respectively to dark matter, dark energy and cosmological inflation. There is also strong but not absolutely conclusive evidence that anti-matter behaves exactly the same as matter with respect to gravity. But, the smallest scales at which GR has been tested experimentally are on the order of millimeters which are many, many orders of magnitude larger than the scales at which uncertainty in the location of quanta become relevant in most cases. There is some evidence, although not sufficient to rule out the null hypothesis of a cosmological constant, that dark energy changes over time rather than being a cosmological constant. See, e.g.
http://backreaction.blogspot.com/2017/06/if-tensions-in-cosmological-data-are.html
Thus, there is not any experimental evidence that covers the nature of the gravitational field due to an entity in spatial superposition as a result of its quantum nature, nor is there any experimental evidence of beyond GR theories of gravity. This has pretty much exclusively been explored on a theoretical basis, and perhaps other commenters can suggest review articles on the topic.
There are a lot of logical reasons why some sort of quantum gravity theory must exist (although even that is not a completely consensus view), but the places where GR and the Standard Model are incompatible are areas where experimental evidence is not available.
Quantum gravity concepts like Hawking radiation call upon a jerry rigged mix of classical and quantum concepts outside the context of a larger theory and one reason that there are huge debates over issues like the "information paradox" and the "no hair theorem" related to black holes is that there is no rigorous larger theory that definitively fuses GR and the Standard Model.
Is it known (or generally presumed) that photons exert gravitational attraction through the stress-energy tensor at all points in space related to the probability of detection at each position?
There is strong evidence that photons exert gravitational attraction through the stress-energy tensor in Einstein's field equations and is likewise subject to gravity. This is basically a consensus view that is not seriously disputed.
Your question goes further, however, to the localization of the gravitational force of a photon in light of the fact that in quantum mechanics, the position of a photon cannot be known exactly.
This beyond the domain of applicability of general relativity and the means by which one should integrate the quantum nature of individual particles whose position is uncertain and is not a consensus matter in quantum gravity, although the difference between using quasi-classical photons and truly quantum photons in almost all quantum gravity models would be immaterial even if it were considered.
The precision of classical tests of GR interacting with photons and the behavior of quanta in Earth's gravitational field, rule out the possibility that considering this would have huge phenomenological effects.
Is this an area of Quantum Gravity which is well understood or subject to debate?
There is no area of quantum gravity which is well understood.
There are two main schools of quantum gravity research - one rooted in string theory and focusing on the behavior of a spin-2 massless graviton in 10-11 dimensional space (sometimes with a low energy approximation of Supergravity (SUGRA)) and the other focusing on the quantization of space-time itself (loop quantum gravity (LQG) and kindred approaches like spin-foams and causal dynamical triangles).
These approaches are so profoundly different in their mechanism and framing of issues that pretty much all issues in quantum gravity are subject to debate.
