Let me try to be more clear.
A statute of limitations tells you how long after a crime was committed (or depending upon how a statute is written, how long after the crime was discovered to have been committed) you can still charge a person with that crime.
That has nothing to do with what penalty will apply to a person convicted. The question that has arisen was whether the new statute enacted in 2023 making certain CSAM death-penalty eligible would be applicable to the penalty for crimes committed prior to enactment. In general, it is not possible to retroactively apply a penalty to a crime that was committed prior to the penalty becoming available - i.e., he would not be death penalty eligible for crimes committed prior to that new statute's effectiveness.