Which are mediated (biologically) how? (rhetorical question)
I assume when you say "rhetorical" you're assuming there is no plausible mechanism. If so, I would suggest you have a look at Noakes and Boksem's reviews. It has been shown that in athletes, psychological factors significantly influence fatigue, which appears to be through connections between the insular cortex and the motor cortex. Also, animal experiments have shown that psychological factors significantly influence whether activity takes place (only taking place if the benefits outweigh the costs). The brain regions responsible have direct control over the HPA axis and ANS.
And if you look at Ben-Zvi (2009) and Gupta (2007) you'll see they predict that there is a state where the HPA axis can get stuck in an abnormal state. Cort wrote a story about this back in 2014 (quoting Broderick).
I'm surprised that anyone cares about effect sizes when there is no control. As Neuroskeptic said when specifically asked about this: generally that's meaningless. That's why you need a control. Within-group D = natural improvement + regression to the mean + placebo effect + real effect. Real effect is generally only a small % of the within group effect, only a placebo controlled study can reveal that.
There were two groups: UK and NL, which had extremely different effect sizes (0.33 vs 0.99). That's certainly worth looking into.
The key is to use a combination of objective measures, including fitness testing, actigraphy, neuropsychological testing and to set composite measures of improvement (eg if step count is normal, then improvement on that is not required). Jonathan Edwards had some stuff to say about how outcome measures could be improved (and how composite measures are sometimes used in other trials for other medical conditions - even when it means the end result seems less impressive). But actigraphy is more than step count and the patterns (eg day to day variation and intensity of exercise are much more revealing than total step count).
But studies show that actigraphy results are not significantly different between CFS and control groups, so it doesn't look like it would be a useful measure. We really need to wait until there is an agreed biomarker. Perhaps something like measuring R-R after exercise.
So when doing less psychologically demanding activities, we answer differently on questionnaires. That's great, but it doesn't mean that person's physical health has improved.
I'm not sure what you mean by "psychologically demanding". They certainly weren't less mentally demanding. Perhaps a better term would be "psychologically damaging". Everyone should avoid psychologically damaging activities, especially CFS patients (and recovered patients).
I agree that we definitely need a definitive measure of recovery, but that isn't available yet. In the absence of that, questionnaires are about the best we have.
Are you skeptical that people can recover? Or skeptical that people can recover from exercise or psychological treatment?