That's definitely true too -- the rates of mental illness are something like doubled in the base population. But the frequency for people who have been sick is much higher than the general population, even accounting for the spike in overall mental illness.
For sure, this needs study too. There have been studies of those who were given treatment though and it shows a correlation. We don’t know, for sure, that COVID-19 is the direct cause of mental issues or a side effect but it’s been recorded in a sample.
I think a study of a general population sample for mental health issues with or without a prior COVID-19 diagnosis would show how varying the COVID-19 patients experiences are vs how everyone else is fairing.
I’m not a scientist or a therapist so I don’t know the exact approach to use to do the comparison but I suspect it could be done.