I've a hunch Long Covid causes lowering of thyroid activity, thus making people at the very least sub-clinically hypothyroid (or maybe full-blown) - brain fog (and fatigue and a slew of other symptoms mentioned in connection with long Covid) are all hypo symptoms. Also, Vitamin B12 deficiency can cause brain fog too. I wouldn't be surprised if a bad case of Covid depletes B12 as well as other nutrients. All this causes the symptoms being reported, I feel. A number of people I know with hypothyroidism have had their thyroid labs show disruption after being vaccinated (they've reported a return to normality after 2-3 months). I suspect if you have Covid badly and the thyroid is affected, this effect carries on for far longer.
I am curious as to what 'help' governments have in mind! Considering how dreadfully they diagnose and treat hypothyroidism and ME/CFS, I can hardly wait to see!