Like, if I had to bet money on it, I'd wager that "long flu" and even "long cold" are real things that happen at least sometimes, but just haven't gotten much attention (and, to be fair, they might also be less common, or less-commonly-as-severe, if they are real).
Also, n=1, but I had a bout of bacterial laryngitis a few weeks ago (was briefly intubated for elective surgery—apparently this is a common side effect) and I'm still feeling a little breathless/cough-y despite having hacked up every last bit of phlegm and finished a full course of antibiotics. Doesn't seem shocking that my lungs would take a bit to recover, even if the bacteria in question have already cleared out.
Anecdotally, for people I know, it would take six weeks to half a year to resolve.
My own speculation is that it's autoimmune, simple due to having it seen resolved when people were vaccinated. However, "anecdote" is not the plural of "data," and it just as well be unrelated.
There are wonky changes to organs during covid, which many doctors speculate are the root cause.
In either case, I'm unaware of any mainstream theories where paxlovid would be likely to help.
Footnote: That's a 180 turn-around from state-of-the-art science a year or so ago. At the time, we thought there were individuals where it persisted (evidence in immunocompromised), but nothing like this.