Not sure about the ME/CFS thing, but "post-infectious syndrome" is literally what its name says it is which makes it a larger category that "long covid" would taxonomize under.

https://pubmed.ncbi.nlm.nih.gov/40627388/#&gid=article-figur... (figure one)

In the limit, there's no difference between a scientific fact and an unfalsified hypothesis. I'm not aware of anyone falsifying this one, and it's over five years old, so I'm going to say "scientific fact".

At this point, even if it is falsified, that falsification will probably take the form "here is an exception to the general rule", like how we still use Newton's law of gravitation even though it was falsified by Urbain Le Verrier's 1859 observations of Mercury.