[data_acquired]

> due to mutations during your lifespan, genetic diversity within your body increases, which increases the prevalence of genes that cause individual cells and tissues to compete with one another rather than cooperating; in the extreme, we call this 'cancer'

This is a good summary. Only thing to keep in mind is that an increase in genetic diversity need not imply a unidirectional march towards cancer, but an increase in risk. One of the most interesting paradoxes of cancer initiation research currently is the presence of "cancer-causing" mutations in phenotypically normal cells for decades prior to the appearance of the first cancer cell (see https://pubmed.ncbi.nlm.nih.gov/27059373/ for instance).

What's remarkable to me about this aging study and others like it is that they are able to reverse some aspect of aging despite the accumulation of genetic diversity with age as you point out. Perhaps what they're reversing was never really dependent on mutation accumulation with age, or that the presence of mutations does not fully explain the age-related degeneration they're interested in reversing.