They indicate that viral RNA was found

I think that may be overstating the case. My understanding is that the test does not look for the virus itself but for some molecules that are believed to be associated with the virus. That means it has no way of telling whether you have the virus now or had it some months ago.

Also, PCR is NOT a test. It just replicates molecules. Every extra ten cycles adds roughly a factor of a thousand to the replication factor so 30 cycles means 1000³ or a billion in round numbers. 40 cycles is a trillion.

The inventor of PCR, Kary Mullis, told us that PCR was not useful as a diagnostic - but we used it anyway.