What I don't believe is that this kind of syndrome is specific to Covid, I suspect it holds for every serious virus you get infected with. The only difference this time is that the medical community is watching.
The fact that Epstein-Barr is causative with MS and HPV is causative with cervical cancer shows that the damage that even fairly mild virii do persists for a very long time.
Any claim that a virus doesn't cause persistent damage simply means you haven't looked very hard.