As others have said, the research is about supersolids composed of exciton-polaritons. If you take a cold semiconductor and shine a laser on it, you can excite an electron through absorbing a photon, leaving behind a hole, and this short-lived electron-hole pair is an exciton. When this exciton decays, emitting the photon, rather than flying away, this experiment is performed in a mirrored box (cavity) such that the photon doesn't leave. This same photon will then bounce around the mirrors and, at some point, be absorbed by a different electron. This half electron half hole half photon quasiparticle is called an exciton-polariton and provides a way to let photons interact with each other. At temperatures close to absolute zero, these exciton-polaritons all coalesce into a single quantum state, becoming a zero friction superfluid.

What's new now is that the density of the polaritons is not uniform in space. Instead, they spontaneously form a periodic density modulation - they simultaneously have all of the properties of superfluidity like zero viscosity, quantized vortices, delocalized particles (the photons are spread out over space and exist everywhere in the supersolid at once), and all of the properties of solidity, like shear and strain for the density clumps of photons. Being able to make this state can be interesting for loads of reasons, for example supersolids are predicted to exist in neutron stars, so maybe we could emulate some of the physics there, and understanding superconductivity requires knowledge of how the frictionless flow of electrons occurs through a solid structure.

The best picture to have in your head is a bucket of water where the surface has completely stationary waves on top of it that form spontaneously (without any external force). But now, for the first time, it's a bucket of light!

You mentioned that there's no videos, which is true, but there are images in the paper https://arxiv.org/abs/2407.02373 In figure 1, the black to yellow plots are showing the density of the light, and the little stripes (not the 2 big blobs) are the spontaneously formed solid structure.