[nradov]

Post viral syndrome has been been recognized for decades and linked to a wide variety of different viruses. So although the exact mechanisms aren't clearly understood there's no reason to think that SARS-CoV-2 couldn't cause similar effects.

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1710789/

But in terms of specific symptoms, a recent study found only a weak correlation between confirmed COVID-19 and brain fog. Other persistent symptoms such as anosmia are much more common.

https://doi.org/10.1038/s41591-022-01909-w

[Madmallard]

This is just a case where the tools we have for examination are lacking and subjective symptom description barring specific indicators is pretty useless from a research standpoint.