I haven’t had COVID (baruch HaShem), but I get a lot of bacterial sinus infections, and if I don’t get into the doctor right away, I can get a lingering bronchitis. I may be absent all other symptoms, but cough for a month. The first time it happened I was in training with the military, and was trying to “suck it up,” and assumed I just had a cold anyway, until it didn’t go away for two weeks, and I was having trouble breathing on runs.
The medic ended up giving me an inhaler for the cough, but what really helped was an OTC cough suppressant, dextromethorphan. Later, I discovered that the Rx cough suppressant tessalon works even better, but insurance doesn’t like to pay for it.
Nothing about this aspect of COVID surprises me at all.