Maybe better as "momentum-energy" than as "energy and momentum". "Stress-energy" is probably better still.
I don't think we have to consider the photons as such because large-photon-number beams sent from, to, and between spacecraft have been shown to deflect around masses in our solar system, sunlight generates measurable radiation pressure (and greybody radiation contributes to the Yarkovsky effect), and because your parent comment just asked about "light".
However, your t and my t can differ if we are in a quasilocally-different gravitational field, or accelerated or boosted with respect to each other. In that case one of us may prefer coordinates where some of the quantity in T^{tt} is instead in T^{tj} (the latter being momentum), or even in the pressure diagonal T^{ij}, i == j, i != t.(e.g. when considering a Shapiro test setting, or a "mirrored box of light").
Although I don't think that much of that particular stack exchange discussion, the accepted answer is right to aim readers at <https://en.wikipedia.org/wiki/Electromagnetic_stress%E2%80%9...>, which is almost wholly classical in its outlook. If one were really keen on thinking about gravitation and sufficiently small numbers of photons, it can get a bit messy or drive one towards the canonical quantization and canonical quantum gravity. As far as I can see nothing at your link goes anywhere close to that, or even really discusses the active or passive gravitational behaviour of an individual photon.
There's better in the sense of correctness, and there's better in the sense of "words that will be useful to someone who has never heard that light can create gravity". My inference is the GGP does not already have a deep technical background in general relativity. This guides the words I choose.
I don't think we have to consider the photons as such because large-photon-number beams sent from, to, and between spacecraft have been shown to deflect around masses in our solar system, sunlight generates measurable radiation pressure (and greybody radiation contributes to the Yarkovsky effect), and because your parent comment just asked about "light".
If we take a look at <https://en.wikipedia.org/wiki/Stress%E2%80%93energy_tensor#/...> and change the 0 indices to "t" (for time), T^{tt} represents quantities conserved across a purely timelike translation, and thus "energy".
However, your t and my t can differ if we are in a quasilocally-different gravitational field, or accelerated or boosted with respect to each other. In that case one of us may prefer coordinates where some of the quantity in T^{tt} is instead in T^{tj} (the latter being momentum), or even in the pressure diagonal T^{ij}, i == j, i != t.(e.g. when considering a Shapiro test setting, or a "mirrored box of light").
Although I don't think that much of that particular stack exchange discussion, the accepted answer is right to aim readers at <https://en.wikipedia.org/wiki/Electromagnetic_stress%E2%80%9...>, which is almost wholly classical in its outlook. If one were really keen on thinking about gravitation and sufficiently small numbers of photons, it can get a bit messy or drive one towards the canonical quantization and canonical quantum gravity. As far as I can see nothing at your link goes anywhere close to that, or even really discusses the active or passive gravitational behaviour of an individual photon.