Inverse pair production with hohlaraum as photon target; is this particular experiment going to be carried out?

Work is in progress. See Experiments underway to turn light into matter on the Imperial website:

In laser facilities in the UK, Imperial physicists are testing an 84-year-old theory which was once thought impossible to prove. The theory of the Breit-Wheeler process says it should be possible to turn light into matter by smashing two particles of light (photons) together to create an electron and a positron. However, past attempts to do this have required the addition of other high-energy particles. Physicists from Imperial College London, led by Professor Steven Rose, came up with a way of testing the theory that did not rely on these added extras in 2014, and today an experiment is running in the hope of turning light directly into matter for the first time. Professor Rose said: “This would be a pure demonstration of Einstein’s famous equation that relates energy and mass: E=mc², which tells us how much energy is produced when matter is turned to energy. What we are doing is the same but backwards: turning photon energy into mass, i.e. m=E/c²”...

Also see this reportage from Science Alert:

These lasers will be used to create the photons that are going to be smashed together. Inside a target chamber, electrons are fired at a slab of gold to produce a beam of high-energy photons. Next, a second high-energy laser is fired into a tiny gold tube called a hohlraum to create a thermal radiation field. The photon beam is then directed through the hohlraum, and the photons from the two sources collide. If it works, the team will be able to detect charged positrons from those collisions...