There's a fairly established and uncontroversial mechanism for light to create gravitational waves... by turning the light into a black hole. Energy and mass are interchangable, photons are affected by gravity thus are gravitationally interacting particles, and if you put enough energy in the form of photons inside a sufficiently small area, the energy density can be equivalent to the mass density required to create a black hole. These "artificial" (because no one has a good explanation how these could ever happen naturally) black holes even have a cool nickname, you call a black hole created this way a Kugelblitz.

But your understanding of the energy involved is still correct... and while reading the pre-print paper this article is writing about https://arxiv.org/pdf/2309.04191.pdf while very full of lots of concrete math involving electromagnetic and gravitational waves it becomes clear where they are starting to speculate a little in section 4, the "FURTHER EXPERIMENTAL
CONSIDERATIONS" part.

To put it mildly... the laser facilities this paper mentions are already the most Death Star like things we've ever built... complete with the fact that we only get all that power when we combine the beams. What this paper is outlining is if these were upgraded using some technology that seems sound, but is still somewhat experimental (likely in large part to remain experimental for some time due to its limited use, the market for ludicrously powerful lasers is... kinda small)... then theoretically these facilities could perform an experiment that could generate a localized gravitational wave pulse that is at its source as strong or in the case of the latest next generation facility being built in Shanghai actually stronger, than some of the gravitational waves we have detected from cosmic events.

Important caveats though, the paper is dealing with a classic "radiated power" vs "received power" situation in a very casual way for informed educated audience. If you skimmed you could easily miss them suggesting locating new gravitational wave detectors near these high power laser facilities, or that theoretically it might be possible to use the lasers themselves to measure it due to how labyrinthine the laser beamlines at these facilities are to begin with. The best case, they have a wave source that could emit with a gravitational wave "power" one order of magnitude stronger at its source than what we know we can currently receive with operating gravitation wave observatories, which are not located anywhere near the current facilities, and with the case of the SEL next gen in Shanghai, will actually be further away since at least the National Ignition Facility is on the same continent as a gravitational wave observatory. 2870 miles / 4619 km from the upcoming Indian gravitational wave observatory facility which is coincidentally going to be finished about the same time as China's new high energy laser facility in Shanghai "2030s" So while there's a lot of "if everyone wants to play nice and doesn't mind some potentially expensive upgrades" and a small dose of "some also new detectors might be needed too" behind this, it is fundamentally sound and pretty clever.

Now what's interesting is that were still "sneezing" as far as cosmic energy levels goes even with these new facilities and PetaWatt pulse powers... The background of the Station of Extreme Light, the new laser facility in Shanghai includes a mention that it may demonstrate the Schwinger effect https://en.wikipedia.org/wiki/Schwinger_effect... which is kind of like (but not quite the same as) the Pair Production process that causes big supernovae in some stars https://en.wikipedia.org/wiki/Pair-instability_supernova... basically at a certain point, all the photons that normally work their way out of a star creating the "photon pressure" that keeps the star from getting crushed by gravity, they start having too much energy, and now instead of bouncing (strictly absorption and re-emission) from one atom to the next suddenly instead of re-emitting a photon its "easier" to chuck out a positron instead, which puts everything out of balance, and soon the star is collapsing in on itself fast enough that its going to blow itself to bits in a very pretty supernova. Except the Schwinger effect is one of those fun quantum field "background noise" type things where this just sort of happens everywhere at an extremely low rate in proportion to how many photons there are and how strong the field is... so a lot more photons, like from the new laser, and hey maybe we'll see this fun new effect we predicted ages ago.

But if we start extrapolating up a bit to get some good examples of how much light you need to really make some impact on the gravity of a region of spacetime... lets compare how much laser power we need to pump through the figurative eye of the needle to go from a gravitational "wave" to making our own very tiny Kugelbliz. If we want a black hole that lasts just a single second before evaporating from Hawking radiation, then we have to put 2.051×10^22 Joules (to help anyone picturing this, 4903 GigaTons of TNT, or roughly equivalent to all the solar energy that hits the side of the earth facing the sun for a whole 36 hours) into an area 3.39×10^(-22) meters across, just 339ym, that's 339 yoctometers, and our itsy bitsy black hole would weigh 228,231.664kg, just a bit over 228 metric tons... To focus the energy in that area we would need similarly tiny gamma ray photons... and the entire thing becomes quite theoretical. Its an odd problem in that to make it more practical from an engineering perspective, we need to make a bigger black hole which requires more energy! and to get a stable black hole, one that would absorb enough cosmic microwave background photons to avoid evaporating, in a fun coincidence we would have to make a black hole with a mass about the same as the Moon, and I'll leave the exact math to the reader, but obviously its going to be a lot more photons to make approximately 73×10^21 kg worth of energy.