There are ongoing assessments of overall morbidity and mortality from government sources such as here and here.. They are long reads. Whilst media and government may not be highlighting this there are folk behind the scenes looking at it.
In the above there are efforts to numerate the morbidity etc. Long covid is a different issue, like other post viral syndromes such as Chronic fatigue syndrome (CFS/ME) or indeed many chronic conditions like pelvic pain. If diagnostics can’t pinpoint something “wrong” they are difficult to deal with. Diagnosis of such conditions then relies on clusters of symptoms and other assessments such as trial treatments to see effects (if it helps). This often leads to such conditions being assigned to psychosomatic causes, “it’s all in your head.” Undoubtedly some are but equally undoubtedly many are not and this can lead to people getting (pissed) fobbed off further complicating the issue. I’m not sure long covid will fit this pattern as there some promising investigations.