If the FPR is very low, the FNR rate doesn't really matter if you get a positive result (unless the pre-test probability is very low, which is not the case here)
While I am quite skeptical of the claims linked above, that link does indeed cover the FNR at the FPR of 0.005, and finds it broadly to be on the same order of magnitude, i.e. also below 0.005.
If the FPR is very low, the FNR rate doesn't really matter if you get a positive result (unless the pre-test probability is very low, which is not the case here)
While I am quite skeptical of the claims linked above, that link does indeed cover the FNR at the FPR of 0.005, and finds it broadly to be on the same order of magnitude, i.e. also below 0.005.