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.