If they were *not* contemporaneous cases, the comparison would be between CFR of new variant and average CFR of old variant, which would be weighted by the early lack of current treatment, meaning the CFR is of the new variant is whatever-percent worse than that (i.e. more dire).
You mention that all cases occurred 'within a timeframe', which I take to mean at least somewhat contemporaneous - so it's not an issue. If the time window was mentioned, I missed it. Sorry 'bout that.