While it's appealing to believe Pinker, his treatment of statistics and probability of war has been debunked. For a mathematical analysis of the history of war see Cirillo and Taleb's paper "On the statistical properties and tail risk of violent conflict" (https://www.fooledbyrandomness.com/violence.pdf).

From the paper: "Accordingly, the public intellectual arena has witnessed active debates, such as the one between Steven Pinker on one side, and John Gray on the other concerning the hypothesis that the long peace was a statistically established phenomenon or a mere statistical sampling error that is characteristic of heavy-tailed processes, 16] and [27]–the latter of which is corroborated by this paper."

Skeptically.

Pinker has been called out for cherry picking by numerous other authors, and particularly Graeber/Wengrow who are a duo of academic anthropologist and archaeologist respectively. Another is Christopher Ryan. In both cases well reasoned counterarguments are poised against Pinker's reasoning.

The only thing I know about the book is from this article https://acoup.blog/2021/10/15/fireside-friday-october-15-202... which recommends Azar Gat, War in Human Civilization instead.