Long COVID, from what I can tell / have read, is acknowledged by research[1][2]. The mechanism of it, and what is the best treatment for the people suffering from it, I think, are still the subject of ongoing research.
If you look closely at what those studies actually survey and how that data is collected, it's clear that many possible co-morbid conditions aren't adequately filtered out. There is _no_ objective test or evidence-based protocol that can conclusively diagnose "long COVID." Doctors must rely on checklists of broad symptoms and the patient's word. The CDC page you linked mentions this under "Data for Long COVID:"
>For example, some studies look for the presence of Long COVID based on self-reported symptoms, while others collect symptoms and conditions recorded in medical records. Some studies focus only on people who have been hospitalized, while others include people who were not hospitalized.
Can serious health conditions can arise as a lasting consequence of infection? Absolutely. Can we easily distinguish between those and other symptoms or conditions which may arise out of stress, anxiety, other unrelated conditions, or symptoms which in some (not all) cases may be psychosomatic? Can we accurately draw conclusions as to how many long-COVID patients there are in total, then apply that conclusion in other areas with confidence as the GP commenter has done? Not yet.