Author here. I could have worded this part better.

I probably bill about 5 hours a day, give or take. The 40 hours I referenced encompasses everything that goes into freelancing including my client work, not just the client work itself.

Work hours seemed an unlikely cause for the burnout to me because I've worked at least that my entire career (and in previous jobs many more hours) without even a hint of burnout. I'll never know the true cause, but I suspect it's a combination of the factors I mentioned in the post.