The cohort used for the study was overwhelmingly white and female (95%+ for both), so I think your first point is fair, its not possible to generalize to the population from this one study. That said, in these groups, that study did definitely find that long covid was strongly correlated with preexisting psychological conditions:

>All types of distress were significantly associated with increased risk of post–COVID-19 conditions in a dose-dependent manner after adjustment for demographic factors (probable depression, RR, 1.39 [95% CI, 1.19-1.63]; probable anxiety, RR, 1.47 [95% CI, 1.27-1.70]; very worried about COVID-19, RR, 1.43 [95% CI, 1.22-1.68]; highest quartile of perceived stress, RR, 1.50 [95% CI, 1.21-1.86]; lonely some of the time or often, RR, 1.35 [95% CI, 1.11-1.65]; all P < .01 for trend)

This is consistent with other studies, e.g.

https://www.acpjournals.org/doi/10.7326/M21-4905

>Increased risk for PASC was noted in women and those with a history of anxiety disorder.

As an aside, the inception of the "condition" is always worth considering in any discussion of long covid:

https://www.wsj.com/articles/the-dubious-origins-of-long-cov...