"Long COVID" is a thing, but is it something unique and specific? Probably not:
https://www.vox.com/22298751/long-term-side-effects-covid-19...
As for ME/CFS being psychosomatic, that's a bit more controversial, with doctors on either side. Nothing is proven either way. Still, symptoms such as fatigue and brain fog are consistent with ME/CFS.
We like to dismiss such symptoms when it is convenient, e.g. when it occurs as a side-effect of a vaccine, while taking it rather serious when it occurs after some hyped-up new illness such as COVID. In either cases, it could simply be the Nocebo effect at work.