The most plausible reason is that many of those reported symptoms were psychosomatic.
Also, "placebo effect" is real. "Reversion to the mean" is also real.
None of those explanations are "psychosomatic".
Take the group off the drug and survey them in 30-90 days for long-COVID symptoms.
You could also play around with control groups, for example perhaps one control group is asked not to watch or read any news programming related to COVID. I think the results would be revealing.
Public interest in the putatively psychosomatic Morgellons disease spiked after Joni Mitchell said she had it. There was an outpouring of support for Mitchell, and criticism of Big Pharma, the government, and the media for not treating Morgellons with more gravity.