Can you dig out the specific reference to Adam and Eve in that book?
Y Adam is most likely Noah (or his sons)
MtDNA Eve is the mother of all living.
As I noted before, linking mtDNA and Y-Chromosomal DNA LCA to people in the Bible is without purpose. They bear no relation. Those terms were adapted from what is the common mythology of the West. That said, there is a significant discussion in the
book about using those portions of the Genome to understand human history. Chapters 1 and 10.
Re: The article from Nature on the date of the oldest Y-Chromosome, see:
Study Says Oldest Known Human Y-Chromosome Branch Dates to 338,000 Years Ago | Genetics | Sci-News.com
Reich uses the 380,000 years ago date in his book.
The conclusion of the estimated smallest bottleneck in the human population is extrapolated from facts.
Fig. 5 on p. 16 (how to date age differences between genes) Source: S. Mallick et. al. “The Simons Genome Diversity Project: 300 genomes from 142 Diverse Populations,” Nature 538 (2016) 201-6.
Li & Durban “Inferring Human Population History from Individual Whole-Genome Sequences” Nature 475 (2011): 493-96.
Those are just a couple of the many sources Reich used for the book. He breaks down the current data as of 2017/18 by region, so you get a thorough overview of what was happening in Europe, India, The Americas, East Asia, and Africa.
As I noted before, Swamidass praised the book linked in my OP in the second video that you linked.