https://en.wikipedia.org/wiki/Mercury_laser
https://www.laserfocusworld.com/test-measurement/research/ar...
The second link has more details, but they show a 0.7% efficient NIF vs. a 7% efficient Mercury laser in the tiny little chart graphic -- which would reduce the energy for this experiment from 285MJ to 28MJ. This is way outside my area of expertise, but from what I understand, the same general tech that LLNL used to generate the HAPLS for Europe's laser research could be applied to the Mercury-like lasers and increase efficiency even further.
https://www.techbriefs.com/component/content/article/tb/insi...
[0]https://en.wikipedia.org/wiki/National_Ignition_Facility#
Since a lot of modern laser research now overlaps with advanced semiconductor manufacturing, the competing systems are much more mature. Here's a good rundown, but experts think that it's plausible to use even up to 20% efficient systems. Rather than using the laser to first generate xrays - these "direct drive" systems deposit the energy from the lasers directly on the pellets.
https://physicstoday.scitation.org/do/10.1063/pt.6.2.2021102...
Yes, I'd agree with that statement that it's only an engineering problem, but with a laser energy of 2 million joules and a fusion yield of only 3 million joules and an overall input of nearly 300 million joules to produce the lasers then I've no expectation of ever seeing a total net positive output in my lifetime let alone fully established working fusion plants providing power to ordinary customers.
Moreover, compare the overall 'negative' efficiency of this experiment with the actual positive efficiencies of existing generation systems: solar: 20+%, combustion: 20%-40%, mechanical/electrical turbine: >97% and so on and we see there's three or so orders of magnitude to catch up upon.
The task may not be impossible but don't hold your breath.