Epidemiological indicators (e.g. reproduction numbers and epidemicity indices) describe long- and short-term behaviour of ongoing epidemics. Their evolving values provide context for designing control measures because maintaining both indices below suitable thresholds warrants waning infection numbers. However, current models for the computation of epidemiological metrics do not consider the stratification of the pathogen into variants endowed with different infectivity and epidemiological severity. This is the case, in particular, with SARS-CoV-2 infections. Failing to account for the variety of epidemiological features of emerging variants prevents epidemiological indices from spotting the possible onset of uncontrolled growth of specific variants, thus significantly limiting the prognostic value of the indicators. Here, we expand an existing framework for the computation of spatially explicit reproduction numbers and epidemicity indices to account for arising variants. By analysing the data of the COVID-19 pandemic in Italy, we show that embedding additional layers of complexity in the mathematical descriptions of unfolding epidemics reveals new angles. In particular, we find epidemiological metrics significantly exceeding their thresholds at the emergence of new variants. Such values foresee a recrudescence in new infections that only becomes evident after emerging new variants have effectively replaced the previous active strains. The demography of the variant composition flags the presence of specific strains growing more rapidly than the total number of infections generated by all variants combined. Variant-aware epidemiological indicators thus allow to engineer better control measures tailored to the shifting patterns of severity and evolving features of infectious disease epidemics.