People are claiming "long covid" for a virus that's been around for <1 year, so presumably the prevalence of this "long covid" could be studied?
As with any other early stage research relying heavily on self reported symptoms, the prevalence figures are not well established and the mechanisms causing it not yet understood, but they don't look like flu.
[1]https://www.bmj.com/content/371/bmj.m3981, https://evidence.nihr.ac.uk/wp-content/uploads/2020/10/Livin...
Long COVID is unproven and anecdotal and seems to be more likely to be psychosomatic in most but not all cases.