The linked paper -- https://arxiv.org/pdf/2212.11319.pdf -- isn't about measuring dark energy at all. (It's using data from a study meant to do that, but it's looking at something else.)
Also, > This phenomenon has various names: the quantum foam, the spacetime foam, vacuum fluctuations.
This confuses two different phenomena. The vacuum fluctuation of known quantum fields (electromagnetic, electron, Higgs, etc.) is what is thought to give rise to the cosmological constant/dark energy, and is what this article is about. (A limited version of it involving the electromagnetic field produces the Casimir effect, which has been measured.) "Spacetime/quantum foam" is the hypothetical fluctuation of spacetime itself, assuming a quantum theory of gravity. It has nothing to do with dark energy.