It is worth noting here, as you didn't say it explicitly, that COVID labs routinely report positives as late as 40 cycles.
“Most tests, like the Broad Institute test used by MIT, use a 40-cycle protocol. If the virus isn’t detected within 40 amplification cycles, the test result is negative. If viral RNA is detected in 40 cycles or less, the PCR machine stops running, and the test is positive. Because you received a positive result, we know that the test detected the virus in your sample by the time it reached its 40-cycle limit.”
https://medical.mit.edu/covid-19-updates/2020/11/pcr-test-re...